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diff --git a/old/52052-0.txt b/old/52052-0.txt deleted file mode 100644 index ea0f10c..0000000 --- a/old/52052-0.txt +++ /dev/null @@ -1,7012 +0,0 @@ -The Project Gutenberg EBook of The Puzzle King, by John Scott - -This eBook is for the use of anyone anywhere in the United States and most -other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms of -the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you'll have -to check the laws of the country where you are located before using this ebook. - - - -Title: The Puzzle King - -Author: John Scott - -Release Date: May 12, 2016 [EBook #52052] - -Language: English - -Character set encoding: UTF-8 - -*** START OF THIS PROJECT GUTENBERG EBOOK THE PUZZLE KING *** - - - - -Produced by MWS, Paul Marshall and the Online Distributed -Proofreading Team at http://www.pgdp.net (This file was -produced from images generously made available by The -Internet Archive) - - - - - -Transcriber's Notes: - - Underscores "_" before and after a word or phrase indicate _italics_ - in the original text. - Equals signs "=" before and after a word or phrase indicate =bold= - in the original text. - The carat symbol "^" is used to indicate a superscript. - Small capitals have been converted to BLOCK capitals. - Antiquated spellings have been preserved. - Typographical errors have been silently corrected but other variations - in spelling and punctuation remain unaltered. - Answers are provided at the end of the book to numbered questions, - however in the original text, numbers 237 to 241 were omitted - for some reason. - - “LAUGH AND GROW FAT.” - - - - - THE PUZZLE KING. - - - AMUSING ARITHMETIC. - BOOK-KEEPING BLUNDERS. - COMMERCIAL COMICALITIES. - CURIOUS “CATCHES.” PECULIAR PROBLEMS. - PERPLEXING PARADOXES. - QUAINT QUESTIONS. QUEER QUIBBLES. - SCHOOL STORIES. - INTERESTING ITEMS. - - Tricks with Figures, Cards, Draughts, Dice, Dominoes, - Etc., Etc., Etc. - - By JOHN SCOTT, - - Author of “How to Become Quick at Figures,” “Doctrine of Chance,” - “Tank Calculator,” “Cyanide Vat Calculator,” &c., &c. - - INSTRUCTIVE and AMUSING. - - Copyright. - - Brisbane, - H. J. DIDDAMS & CO., Printers and Publishers, Elizabeth Street, - MDCCCXCIX. - - - - -PREFACE. - - - A puzzle is not solved, impatient sirs, - By peeping at its answer in a trice: - When Gordius, the ploughboy King of Phrygia, - Tied up his implements of husbandry - In the far-famed knot, rash Alexander - Did not undo by cutting it in twain. - -It is hoped that this little book may prove useful, not only in -connection with puzzles for home amusement, but that by inducing -people to consider the various difficulties met with in business and -trade some at least may be led to greater success in dealing with the -practical puzzles and problems of everyday life. - -It is the special desire of the author to produce a “sugar-coated -mathematical pill,” as he feels convinced that many can more easily -grasp the truth when it is put before them in a light manner than -when brought forward in the usual orthodox fashion. - -No pains have been spared to make the PUZZLE KING the best -of its kind yet produced, and the author here wishes to thank his -many friends who have so kindly assisted him. It would be well-nigh -impossible to individualize; but especial thanks are due to Thos. -Finney, Esq., M.L.A. (Brisbane), for the interest he has manifested -throughout, and the kindly help he has so often rendered the author. - -It might afford our readers some pleasure to know that this work -is entirely Australian. The printers, artist, and author are all -colonial-born, and the production of the former two, at any rate, -will compare favourably with that of any others. - -The engravings throughout have been in the hands of Mr. Murray Fraser -and staff, whose experience in this special art has tended to make -the book more attractive than it otherwise would have been. - -The author is not above receiving any suggestions or contributions in -the way of peculiar puzzles or commercial comicalities, which might -enhance the value of the book. Intending contributors are invited -to communicate to the address given below, and can rest assured -that they will be remunerated according to the merits of their -communications. - - THE AUTHOR. - _44, Pitt Street, Sydney._ - -_Refer to Appendix for Answers to numbered Problems._ - - - - -READING BIG NUMBERS. - -Wonderful Calculations. - - -Although we are accustomed to speak in the most airy fashion of -millions, billions, &c., and “rattle” off at a breath strings of -figures, the fact still remains that we are unable to grasp their -vastness. Man is finite--numbers are infinite! - - ONE MILLION - -Is beyond our conception. We can no more realise its immensity, than -we can the tenth part of a second. It should be a pleasing fact -to note that commercial calculations do not often extend beyond -millions; generally speaking, it is in the realm of speculative -calculation only, such as probability, astronomy, &c., that we are -brought face to face with these unthinkable magnitudes. - -Who, for instance, could form the slightest idea that the odds -against a person tossing a coin in the air so as to bring a head -200 times in succession are -160693804425899027554196209234116260522202993782792835301375 -(over I decillion, &c.) to 1 against him? Suppose that all the men, -women and children on the face of the earth were to keep on tossing -coins at the rate of a million a second for a million years, the -odds would still be too great for us to realise against any one -person succeeding in performing the above feat, and yet the number -representing the odds would be only half as long as the one already -given. - -Or, who could understand the other equally astounding fact that -Sirius, the Dog-star, is 130435000000000 miles from the earth, or -even that the earth itself is 5426000000000000000000 tons in weight. - - WHAT IS A BILLION - -In Europe and America, the billion is 1,000,000,000--a thousand -millions--but in Great Britain and her Colonies, a billion is -reckoned 1,000,000,000,000--a million millions: a difference which -should perhaps be worth remembering in the case of francs and dollars. - -One billion sovereigns placed side by side would extend to a distance -of over 18,000,000 miles, and make a band which would pass 736 times -round the globe, or, if lying side by side, would form a golden belt -around it over 26 ft. wide; if the sovereigns were placed on top of -each other flatways, the golden column would be more than a million -miles in height. - -Supposing you could count at the rate of 200 a minute; then, in -one hour, you could count 12,000--if you were not interrupted. Well, -12,000 an hour would be 288,000 a day; and a year, or 365 days, -would produce 105,120,000. But this would not allow you a single -moment for sleep, or for any other business whatever. If Adam at -the beginning of his existence, had begun to count, had continued to -count, and were counting still, he would not even now, according to -the usually supposed age of man, have counted nearly enough. To -count a billion, he would require 9,512 years, 342 days, 5 hours and 20 -minutes, according to the above reckoning. But suppose we were to -allow the poor counter twelve hours daily for rest, eating and sleeping, -he would need 19,025 years, 319 days, 10 hours and 40 minutes to -count one billion. - - A comparison-- - One million seconds = less than 12 days - " billion " = over 31,000 years - - -A GOOD CATCH. - -1.--Ask a person to write, in figures, eleven thousand, eleven -hundred and eleven. This often proves very amusing, few being able to -write it correctly at first. - -2.--If the eighth of £1 be 3s, what will the fifth of a £5 note be? - - -=BOTHERSOME BILLS=. - -Defter at the anvil than at the desk was a village blacksmith who -held a customer responsible for a little account running: - - To menden to broken sorspuns 4 punse - To handl to a kleffr 6 " - To pointen 3 iron skurrs 3 " - To repairen a lanton 2 " - A klapper to a bel 8 " - Medsen attenden a cow sick the numoraman a bad i 6 " - To arf a da elpen a fillup a taken in arvist 1 shillin - To a hole da elpen a fillup a taken in arvist 2 " - ---------- - Totle of altigether 5 shillins and fippunse. - -That the honest man’s services had been requisitioned for the mending -of two saucepans, putting a new handle to an old cleaver, sharpening -three blunted iron skewers, repairing a lantern, and providing a bell -with a clapper is clear enough; and by resolving “a fillup” into “A. -Phillip,” all obscurity is removed from the last two items, but “the -numoraman a bad i” is a nut the reader must crack for himself. - - -ONE FROM A PUBLICAN. - -He stabled a horse for a night, and sent it home next day with a bill -debiting the owner: - - To anos 4/6 - To agitinonimom -/6 - --- - 5/- - - -A LAUNDRY BILL. - -A tourist in Tasmania, being called upon to pay a native dame of the -wash-tub “OOo III,” opened his eyes and ejaculated, “O!” but the good -woman explained that he owed her just two and ninepence, a big O -standing for a shilling, a little one for sixpence, and each I for a -penny. - - -THE DUTCHMAN’S ACCOUNT. - - Two wax dolls 15/- - One wooden do 7/6 - ---- - Total 7/6 - -The two dolls were 7s 6d each, but one “wouldn’t do;” so, being -returned, it was taken off the account in the above manner. - - -A carpenter in Melbourne who did a small job in an office, made -out his bill: - - To hanging one door and myself 14s. - - -A BILL MADE OUT BY A MAN WHO COULD NOT WRITE. - -[Illustration: This is an exact copy of a bill sent by a bricklayer -to a gentleman for work done. Date, 1798.] - -This is an exact copy of a bill sent by a bricklayer to a gentleman -for work done. Date, 1798. - -The bill reads thus: Two men and a boy, ¾ of a day, 2 hods of mortar, -10s 10d. Settled. - - -A BILL FROM AN IRISH TAILOR. - -To receipting a pair of trousers 5s. - - -QUITE RIGHT. - -At a large manufactory a patent pump refused to work. Several -engineers failed to discover the cause. The local plumber, however, -succeeded, after a few minutes, in putting it in working order, and -sent to the company-- - - To Mending pump 2 0 - " Knowing how 5 0 0 - ------ - Total £5 2 0 - - -A VETERINARY SURGEON’S ACCOUNT. - -To curing your pony, that died yesterday, £1 1s. - - -3. What is the number that the square of its half is equal to the -number reversed? - - -HOW TO GET A HEAD-ACHE. - -[Illustration] - -Naturalists state that snakes, when in danger, have been known to -swallow each other; the above three snakes have just commenced to -perform this operation. The snakes are from the same “hatch,” and -are therefore equal in age, length, weight, &c. They all start at -scratch--that is, commence swallowing simultaneously. They are -twirling round at the express rate of 300 revolutions per minute, -during which time the circumference is decreased by 1 inch. - -We would like our readers to tell us what will be the final result? -Heads or tails, and how many of each? - - -4. A man sold two horses for £100 each; he lost 25 per cent. on one, -and gained 25 per cent. on the other. Was he “quits”; or did he lose -or gain by the transaction; and, if so, how much? - - -A GOOD CARD TRICK. - -The performer lays upon the table ten cards, side by side, face -downwards. Anyone is then at liberty (the performer meanwhile -retiring from the room) to shift any number of the cards (from one -to nine inclusive) from the right hand end of the row to the left, -but retaining the order of the cards so shifted. The performer, on -his return, makes a little speech: “Ladies and gentlemen, you have -shifted a certain number of these cards. Now, I don’t intend to ask -you a single question. By a simple mental calculation I can ascertain -the number you have moved, and by my clairvoyant faculty, though the -cards are face downwards, I shall pick out one corresponding with -that number. Let me see” (pretends to calculate, and presently turns -up a card representing “five”). “You shifted five cards and I have -turned up a five, the exact number.” - -The cards moved are not replaced, but the performer again retires, -and a second person is invited to move a few more from right to -left. Again the performer on his return takes up the correct card -indicating the number shifted. The trick, unlike most others, may be -repeated without fear of detection. - -[Illustration] - -The principle is arithmetical. To begin with, the cards are arranged, -unknown to the spectators, in the following order: - -Ten, nine, eight, seven, six, five, four, three, two, one. - -Such being the case, it will be found that, however many are shifted -from right to left, the _first_ card of the new row will indicate -their number. Thus, suppose _three_ are shifted. The new order of the -cards will then be: - -_Three_, two, one, ten, nine, eight, seven, six, five, four. - -So far, the trick is easy enough, but the method of its continuance -is a trifle more complicated. To tell the position of the indicating -card after the second removal, the performer privately adds the -number of that last turned up (in this case _three_) to its place in -the row--_one_. That gives us _four_, the card to be turned up -after the next shift will be the fourth. Thus, suppose six cards are now -shifted, their new order will be: - -Nine, eight, seven, _six_, five, four, three, two, one, ten. - -Had five cards only been shifted, the _five_ would have been -fourth in the row, and so on. - -The performer now adds _six_, the number of the card, to its place -in the row, _four_: the total, _ten_, gives him the position of -the indicator for the next attempt. Thus, suppose four cards are next -shifted, the new order will be: - -Three, two, one, ten, nine, eight, seven, six, five, _four_. - -The next calculation, 4 and 10, gives us a total 14. The ten is, in -this case, cancelled, and the fourteen regarded as _four_, which -will be found to be the correct indicator for the next shifting. - -It looks more mystifying if the performer be blindfolded, for he can -tell the position of the cards with his fingers. Keeping his hand -on the card, he asks, “Will you please tell me how many cards were -shifted?” As soon as the answer is given, he exhibits the card, and -can continue the trick as long as he pleases. - - -5. Find 16 numbers in arithmetical progression (common difference 2) -whose sum shall be equal to 7552, and arrange them in 4 columns, 4 -numbers in each column--or, in other words, arrange in a square of 16 -numbers that when added vertically, horizontally, or diagonally, the -sum of each 4 numbers will amount to 1888. - - - - -SOME CURIOUS NUMBERS. - - -If the number 37 be multiplied by 3, or any multiple of 3 up to 27, -the product is expressed by three similar digits. Thus-- - - 37 × 3 = 111 - 37 × 6 = 222 - 37 × 9 = 333 - -The products succeed each other in the order of the digits read -downwards, 1, 2, 3, etc., these being multiplied by 3 (their number -of places) reproduce the multiplicand of 37. - - 1 × 3 = 3 - 2 × 3 = 6 - 3 × 3 = 9 - -If it be multiplied by multiples of 3, beyond 27, this peculiarity is -continued, except that the extreme figures taken together represent -the multiple of 3 that is used as a multiplier. Thus-- - - 37 × 30 = 1110, extreme figures, 10 - 37 × 33 = 1221 " " 11 - 37 × 36 = 1332 " " 12 - -The number 73 (which is 37 inverted) multiplied by each of the -numbers of arithmetical progression 3, 6, 9, 12, 15, etc., produces -products terminating (unit’s place) by one of the ten different -figures, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0. These figures will be found in -the reverse order to that of the progression, 73 × 3 produces 9, by 6 -produces 8, and 9 produces 7, and so on. - -Another number which falls under some mysterious law of series is -142,857, which, multiplied by 1, 2, 3, 4, 5, or 6 gives the same -figures in the same order, beginning differently; but if multiplied -by 7, gives all 9’s. - - 142,857 multiplied by 1 = 142,857 - " " 2 = 285,714 - " " 3 = 428,571 - " " 4 = 571,428 - " " 5 = 714,285 - " " 6 = 857,142 - " " 7 = 999,999 - -Multiplied by 8, it gives 1,142,856, the first figure added to the -last makes the original number--142,857. - -The vulgar fraction 1/7 = ·142,857. - -The following number, 526315789473684210, if multiplied as above, -will, in the product, present the same peculiarities, as also will -the number 3448275862068965517241379310. - - The multiplication of 987654321 by 45 = 444444444445 - Do. 123456789 " 45 = 5555555505 - Do. 987654321 " 54 = 53333333334 - Do. 123456789 " 54 = 6666666606 - -Taking the same multiplicand and multiplying by 27 (half 54) the -product is 26,666,666,667, all 6’s except the extremes, which read -the original multiplier (27). If 72 be used as a multiplier, a -similar series of progression is produced. - - -6. In stables five, can you contrive to put in horses twenty-- - In each stable an odd horse, and not a stable empty? - - -“THREE THREES ARE TEN.” - -This little trick often puzzles many:-- - -Place three matches, coins, or other articles on the table, and by -picking each one up and placing it back three times, counting each -time to finish with number 10, instead of 9. Pick up the first match -and return it to the table saying 1; the same with the second and -third, saying 2 and 3; repeat this counting 4; but the fifth match -must be held in the hand, saying at the time it is picked up, 5; the -other two are also picked up and held in hand, making 6 and 7; the -three matches are then returned to the table as 8, 9, and 10. If done -quickly few are able to see through it. - - -7. A man bought a colt for a certain sum and sold him 2 years -afterwards for £50 14s., gaining thereby as much per cent. per annum -compound interest as it had cost him. What was the original price? - - -=Do Figures Lie?= - - -“Figures cannot lie,” is a very old saying. Nevertheless, we can -all be deceived by them. Perhaps one of the best instances of them -leading us astray is the following:-- - -An employer engaged two young men, A and B, and agreed to pay them -wages at the rate of £100 per annum. A enquires if there is to be a -“rise,” and is answered by the employer, “Yes, I will increase your -wages £5 every six months.” “Oh! that is very small; it’s only £10 -per year,” replied A. “Well,” said the employer, “I will double it, -and give you a rise of £20 per year.” A accepts the situation on -those terms. - -B, in making his choice, prefers the £5 every six months. At the -first glance, it would appear that A’s position was the better. - -Now, let us see how much each receives up to the end of four years:-- - - A B - 1st year £100 | 50} 1st year - 2nd " 120 | 55} - 3rd " 140 | 60} 2nd " - 4th " 160 | 65} - | 70} 3rd " - | 75} - | 80} 4th " - | 85} - ---- | ---- - £520 | £540 - - -A spieler at a Country Show amused the people with the following -game:--He had 6 large dice, each of which was marked only on one -face--the first with 1, the second 2, and so on to the sixth, which -was marked 6. He held in his hand a bundle of notes, and offered to -stake £100 to £1 if, in throwing these six dice, the six marked faces -should come up only once, and the person attempting it to have 20 -throws. - -Though the proposal of the spieler does not on the first view appear -very disadvantageous to those who wagered with him, it is certain -there were a great many chances against them. - -The six dice can come up 46,656 different ways, only one of which -would give the marked faces; the odds, therefore, in doing this -in one throw would be 46,655 to 1 against, but, as the player was -allowed 20 throws, the probability of his succeeding would be-- - - 20 - ------ - 46,656 - -To play an equal game, therefore, the spieler should have engaged to -return 2332 times the money deposited. - - -TREBLE RULE OF THREE. - -If 70 dogs with 5 legs each catch 90 rabbits with 3 legs each in 25 -minutes, how many legs must 80 rabbits have to get away from 50 dogs -with 2 legs each in half an hour? - - -8. Suppose a greyhound makes 27 springs whilst a hare makes 25, and -the springs are equal: if the hare is 50 springs before the hound at -the start, in how many springs will the hound overtake the hare? - - -The first Arithmetic in English was written by Tonstal, Bishop of -London, and printed by Pinson in 1552. - - -Two persons playing dominoes 10 hours a day and making 4 moves a -minute could continue 118,000 years without exhausting all the -combinations of the game. - - -A schoolmaster wrote the word “dozen” on the blackboard, and asked -the pupils to each write a sentence containing the word. He was -somewhat taken aback to find on one of the slates the following -unique sentence: “I dozen know my lesson.” - - -9. - I have a piece of ground, which is neither square nor round, - But an octagon, and this I have laid out - In a novel way, though plain in appearance, and retain - Three posts in each compartment; but I doubt - Whether you discover how I apportioned it, e’en tho’ - I inform you ’tis divided into four. - But, if you solve it right, ’twill afford you much delight - And repay you for the trouble, I am sure. - -[Illustration] - - -At an examination in arithmetic, a little boy was asked “what two and -two made?” Answer--“Four.” “Two and four?” Answer--“Six.” “Two and -six?” Answer--“Half-a-crown.” - - -10. A certain gentleman dying left his executor the sum of £3,000 -to be disposed of in the following manner, viz.:--To give to his -son £1,000, to his wife £1,000, to his sister £1,000, and to his -sister’s son £1,000, to his mother’s grandson £1,000, to his own -father and mother £1,000, and to his wife’s own father and mother -£1,000--required, the scheme of kindred. - - -COPY OF LETTER FROM FIRM TO COMMERCIAL TRAVELLER. - - Sydney, - 25th Jan., 1895. - MR. EINSTEIN, Townsville, - DEAR SIR, - -Ve hav receved your letter on the 18th mit expense agount and round -list. vat ve vants is orders, ve haf plenty maps in Sydney vrom vich -to make up round lists also big families to make expenses. - -Mr. Einstein ve find in going through your expenses agount 10s. for -pilliards please don’t buy no more pilliards for us. vat ve vants is -orders, also ve do see 30s. for a Horse and Buggy, vere is de horse -and vot haf you done mit de Buggy the rest on your expenses agount -vas nix but drinks--vy don’t you suck ice. ve sended you to day two -boxes cigars, 1 costed 6/-and the oder 3/6 you can smoke the 6/- -box, but gif de oders to your gustomers, ve send you also samples of -a necktie vat costed us 28/-gross, sell dem for 30/-dozen if you -can’t get 30/-take 8/6, vat ve vants is orders. The neckties is a -novelty as ve hav dem in stock for seven years and ain’d sold none. -My brother Louis says you should stop in Rockhampton. His cousin -Marks livs dere. Louis says you should sell Marks a good bill; dry -him mit de neckties first, and sell mostly for cash, he is Louis’s -cousin. Ve only giv credit to dem gustomers vat pays cash. Don’t date -any more bills ahead, as the days are longer in the summer as in the -vinter. Don’t show Marks any of the good sellers, and finaly remember -Mr. Einstein mit us veder you do bisness or you do nothings at all -vat ve vants is orders. - - Yours Truly, - SHADRACK & Co. - P.S.--Keep the expenses down. - - -11. Two fathers and two sons went into a hotel to have drinks, which -amounted to one shilling. They each spent the same amount. How much -did each pay? - - -12. In a cricket match, a side of 11 men made a certain number of -runs. One obtained one-eighth of the number, each of two others -one-tenth, and each of three others one-twentieth. The rest made up -among them 126 (the remainder of the score), and four of the last -scored five times as many as the others. What was the whole number of -runs, and the score of each man? - - -BRAINS v. BRAWN. - -SCHOOLMASTER--“What is meant by mental occupation?” - -PUPIL--“One in which we use our minds.” - -SCHOOLMASTER--“And a manual occupation?” - -PUPIL--“One in which we use our hands.” - -SCHOOLMASTER--“Now, which of these occupations is mine. -Come, now; what do I use most in teaching you?” - -PUPIL (quickly)--“Your cane, sir!” - -[Illustration] - - -MAGIC ADDITION. - -_To write the answer of an addition sum, when only one line has been -written._ - - 73468 - 52174 } pair - 47825 } - 69341 } pair - 30658 } - ------ - 273466 - ====== - -Tell a person to write down a row of figures. Now, this row will -constitute the main body of the answer. Tell him to write another -row beneath it; you now write a row also, matching his second row in -pairs of 9’s he writes one more row, and you again supply another in -the same manner. Your addition sum will now consist of five lines, -four of which are paired; the first line, or _key_ line, being the -answer to the sum. - -From the unit figure in the _key_ line deduct the number of pairs of -9’s--in this instance two--and place the remainder, 6, as the unit -figure of the answer, then write in order the rest of the figures -in the _key_ line, annexing the 2 to the extreme left; this will -constitute the complete answer. - -It, of course, is not necessary to adhere to two pairs of 9’s; there -may be three, four, or even more; but the total number of lines, -including the _key_ line, must be _odd_, and the number of pairs must -be deducted from the unit figure of the _key_ line, and this same -number be written down at the extreme left. The number of figures in -each line should always be the same. As the location of the _key_ -line may be changed if necessary, the artifice could not easily be -detected. - - -Punctuation was first used in literature in the year 1520. Before that -time wordsandsentenceswereputtogetherlikethis. - -13. Smith and Brown meet a dairymaid with a pail containing milk. -Smith maintains that it is exactly half full; Brown that it is not. -The result is a wager. They have no instrument of any kind, nor can -they procure one by means of which to decide the wager; nevertheless -they manage to find out accurately, and without assistance, whether -the pail is half-full or not. How is it done?--It should be added -that the pail is true in every direction. - -[Illustration] - - -A HINT FOR TAILORS. - -“There, stand in that position, please, and look straight at that -notice while I take your measure.” - - Customer reads the notice-- - “Terms Cash.” - - -=NUMBER 9.= - -If two numbers divisible by 9 be added together the sum of the -figures in the amount will be either 9 or a number divisible by 9. - - Example: 54 - (1) 36 - -- - 90 - -If one number divisible by 9 be subtracted from another number -divisible by 9, the remainder will be either a 9 or a number -divisible by 9. - - Example: 72 - (2) 18 - -- - 54 - -If one number divisible by 9 be multiplied by another number -divisible by 9, the product will be divisible by 9. - - Example: 54 - (3) 27 - ---- - 1458 - -If one number divisible by 9 be divided by another number divisible -by 9, the quotient will be divisible by 9. - - Example: 27)3645 - (4) ---- - 135 - -In the above examples it is worth noting that the figures in each -answer added together continually produce 9. - - (1) 90 = 9 (2) 54 = 9 (3) 1458 = 18 = 9 (4) 135 = 9 - -Also, if these answers be multiplied by any number whatever, a -similar result will be produced. - - Example: 135 x 8 = 1080 = 9 - -If any row of two or more figures be reversed and subtracted -from itself, the figures composing the remainder will, when added, -be a multiple of 9, and if added together continually will result in 9. - - Example: 7362 - 2637 - ---- - 4725 = 18 = 9 - -Tell a person to write a row of figures, then to add them together, -and to subtract the total from the row first written, then to cross out -any one of the figures in the answer, and to add the remaining -figures in the answer together, omitting the figure crossed out; if the -total be now told, it is easy to discover the figure crossed out. - - Example: 4367256 = 33 - 33 - ------- - 4367223 = 27 - -It should be observed that the figures of the answer to the -subtraction when added together equal 27--a multiple of 9; this, -of course, is always the case. Now, suppose that 7 was the figure -crossed out, then the sum of the figures in the answer (omitting -7) would be 20; this number being told by the person, it is easily -seen that 7 must have been crossed out, as that figure is required -to complete the multiple 27. If after the figure has been crossed -out, the remaining figures total a multiple of 9, it is evident that -either a cipher or a 9 must have been the figure erased. - -Multiply the digits--omitting 8--by any multiple of 9, and the -product will consist of that multiple, - - Example: 12345679 36 = 4 x 9 - 36 - -------- - 444444444 - -If a figure with a number of ciphers attached to it be divided by -9, the quotient will be composed of that figure only repeated as many -times as there are ciphers in the dividend; with the same figure as -the remainder. - - Example: 9)7000000 - -------- - 777777-7 - - -EXCUSES. - -“Miss Brown,--You must stop teach my Lizzie fisical torture. She -needs reading and figgers more an that. If I want her to do jumpin -I kin make her jump.” - - -“Please let Willie home at 3 o’clock. I take him out for a little -pleasure, to see his father’s grave.” - - -“Dear Teecher,--Please excuse John for staying home--he had the -meesels to oblige his father.” - - -“Dear Miss----, Please excuse my boy scratching hisself, he’s got a -new flannel shirt on.” - - -“A country schoolmaster received from a small boy a slip of paper -which was supposed to contain an excuse for the non-attendance -of the boy’s brother. He examined the paper, and saw thereon: - - “Kepatomtogoataturing.” - -Unable to understand, the small boy explained to the master that his -big brother had been “kept at home to go taturing”--that is, to dig -potatoes. - - -“Tommy,” said the school teacher, “you must get your father to give -you an excuse the next time you stay away from school.” - -“That’s no use, teacher. Dad’s no good at making excuses; mother -bowls him out every time.” - - -HARVESTING. - -14. A and B engage to reap a field for 90s. A could reap it in 9 days -by himself; they promised to complete it in five days; they found, -however, that they were obliged to call in C (an inferior workman) to -assist them the last two days, in consequence of which B received 3s. -9d. less than he otherwise would have done. In what time could B and -C reap the field alone? - - -15. A man has a triangular block of land, the largest side being 136 -chains, and each of the other sides 68 chains. What is the value of -the grass on it, at the rate of £2 an acre? - - -A school inspector in the North of Ireland was once examining a -geography class, and asked the question: - -“What is a lake?” - -He was much amused when a little fellow, evidently a true gem -of the emerald isle, answered: “It’s a hole in a can, sur.” - -CANVASSER--“I’ve got some signs that I’m selling to -shopkeepers all day long. Everybody buys ’em. Here’s one--“If You -Don’t See What You Want, Ask For It.” - -COUNTRY SHOPKEEPER--“Think I want to be bothered with people -asking for things I ain’t got. Give me one reading “Ef Yeh Don’t See -What Yeh Want, Ask Fer Something Else.” - -[Illustration] - - -16. The number of soldiers placed at a review is such that they could -be formed into 4 hollow squares, each 4 deep, and contain 24 men in -the front rank more than when formed into a solid square. Find the -whole number. - - -In the counting-house of an Irishman the following notice is -exhibited in a conspicuous place: “Persons having no business in this -office will please get it done as soon as possible and leave.” - - -17. - - Upon a piece of cardboard draw - The three designs you see-- - I should have said of each shape four-- - Which when cut out will be, - If joined correctly, that which you - Are striving to unfold-- - An octagon, familiar to - My friends both young and old. - -[Illustration] - - -“I was induced to-day, by the importunity of your traveller,” wrote -an up-country store-keeper to a Brisbane firm, “to give him an order; -but, as I did it merely to get rid of him in a civil manner, and to -prevent my losing any more time, I must ask you to cancel the same.” - - -A CATCH IN EUCHRE. - -18. What card in the game of euchre is always trumps and yet never -turned up? This often puzzles many. - - -RELIGIOUS RECKONING.--(THE NEW JERUSALEM.) - -Revelations xxi. (15)--“_And he that talked with me had a golden -rule to measure the city and the gates thereof and the wall thereof_; - -(16) “_And the city lieth four square, and the length is as large -as the breadth, and he measured the city with the reed twelve thousand -furlongs. The length and the breadth and the height of it are equal._” - -12,000 furlongs = 7,920,000 feet, which cubed = 496793088000000000000 -cubic feet; half of this we will reserve for the Throne and Court of -Heaven, and half the balance for streets, &c., leaving a remainder -of 124198272000000000000 cubic feet. Divide this by 4096 (the cubic -feet in a room 16 feet square) and there will be 3032184375 000000 -rooms. Suppose that the world always did and always will contain -990,000,000 inhabitants, and that a generation lasts 33⅓ years, -making in all 2,970,000,000 every century, and that the world will -stand 100,000 years, totalling 2,970,000,000,000 inhabitants; then -suppose there were 100 worlds equal to this in number of inhabitants -and duration of years, making a total of 297,000,000,000,000 persons. -There would then be more than 100 rooms 16 feet square for each person. - - -19. A man had a certain number of £’s, which he divided among 4 men. -To the first he gave a part, to the second one-third of what was left -after the first’s share, to the third he gave five-eighths of what -was left, and to the fourth the balance, which equalled two-fifths of -the first man’s share. How much money did he have, and how much did -each receive, none receiving as much as £20? - - -ROWING AGAINST TIME. - -20. In a time race, one boat is rowed over the course at an average -pace of 4 yards per second, another moves over the first half of the -course at the rate of 3½ yards per second, and over the last half -at 4½ yards per second, reaching the winning post 15 seconds later -than the first. Find time taken by each. - - -STOCK-BREEDING. - -21. A farmer, being asked what number of animals he kept, answered: -“They’re all horses but two, all sheep but two, and all pigs but -two.” How many had he? - - -A QUIBBLE. - -22. What is the difference between twice one hundred and five, and -twice one hundred, and ten? - - -23. The product of two numbers is six times their sum, and the sum of -their squares is 325. What are the numbers? - - -THE PUZZLE ABOUT THE “PER CENTS.” - -There are many persons engaged in business who often become badly -mixed when they attempt to handle the subject of per centages. The -ascending scale is easy enough: 5 added to 20 is a gain of 25%; given -any sum of figures the doubling of it is an addition of 100%. But -the moment the change is a decreasing calculation the inexperienced -mathematician betrays himself, and even the expert is apt to stumble -or go astray. An advance from 20 to 25 is an increase of 25%; but the -reverse of this, that is, a decline from 25 to 20 is a decrease of -only 20%. - -There are many persons, otherwise intelligent, who cannot see why the -reduction of 100 to 50 is not a decrease of 100%, if an advance from -50 to 100 is an increase of 100%. - -The other day, an article of merchandise which had been purchased -at 10 pence a pound was resold at 30 pence a pound--an advance of -200%. Whereupon, a writer in chronicling the sale said that at the -beginning of the recent depression several invoices of the same class -of goods which had cost over 30 pence per pound had been finally sold -at 10 pence per pound--a loss of over 200%! Of course there cannot -be a decrease or loss of more than 100%, because this wipes out the -whole investment and makes the price nothing. An advance from 10 to -30 is a gain of 200%; but a decline of 30 to 10 is a loss of only -66⅔%. - -A very deserving trader was ruined by his miscalculations respecting -mercantile discounts. The article he manufactured he at first -supplied to retail dealers at a large profit of about 30%. He -afterwards confined his trade almost exclusively to large wholesale -houses, to whom he charged the same price, but allowed a discount of -20%, believing that he was still realising 10% for his own profit. -His trade was very extensive, and it was not till after some years -that he discovered the fact that in place of making 10% profit, as -he imagined, by this mode of making his sales he was realising only -4%. To £100 value of goods he added 30%, and invoiced them at £130. -At the end of each month, in the settlement of accounts amounting to -some thousands of pounds with individual houses, he deducted 20%, or -£26 on each £130, leaving £104, value of goods at prime cost, instead -of £110, as he all along expected. - - -24. Divide 75 into two parts so that three times the greater may -exceed seven times the less by 15. - - -25. What number is that which, being divided by 7 and the quotient -diminished by 10, three times the remainder shall be 24? - - -N.B. - -“Trust men and they will trust you,” said Emerson. “Trust men and -they will bust you,” says the business man. - - 26. - Two years ago to Hobart-town - A certain number of folk came down. - The square root of half of them got married, - And then in Hobart no longer tarried; - Eight-ninths of all went away as well - (This is a story sad to tell): - The square root of four now live here in woe! - How many came here two years ago? - -[Illustration] - - -PECULIARITIES OF SQUARES. - -The following is well worth examining:-- - - 2^2. equals 1 plus 2 plus 1 equals 4 - 3^2. " 4 " 2 " 3 " 9 - 4^2. " 9 " 2 " 5 " 16 - 5^2. " 16 " 2 " 7 " 25 - 6^2. " 25 " 2 " 9 " 36 - 7^2. " 36 " 2 " 11 " 49 - 8^2. " 49 " 2 " 13 " 64 - 9^2. " 64 " 2 " 15 " 81 - 10^2. " 81 " 2 " 17 " 100 - 11^2. " 100 " 2 " 19 " 121 - 12^2. " 121 " 2 " 21 " 144 - - -27. How many inches are there in the diagonal of a cubic foot? and -how many square inches in a superficies made by a plane through two -opposite edges of the cube? - - -FATHER (who has helped his son in his arithmetic at -home)--“What did the teacher remark when you showed him your sums?” - -JOHNNY--“He said I was getting more stupid every day.” - - - A “CATCH.” - -28. - 2 plus 2 = 4 - 2 x 2 = 4 The sum and product are alike. - -Find another number that when added to itself the sum will equal its -square. - -29. A man went to market with 3 baskets of oranges, which he sold at -6d. per dozen; after paying 2s. for refreshments and his coach fare, -he had remaining 7s. The contents of the first and second baskets -were equal to four times the first, and the contents of the first and -half the third were together equal to the second; if he had sold the -second and third baskets at 4d per dozen, he would have made as much -money as he had now remaining. What was the coach fare? - -[Illustration] - - -30. A farmer has a triangular paddock, the sides of which are 900, -750, and 600 links; he requires to cut off 3 roods and 28 perches -therefrom by a straight fence parallel to its least side. What -distance must be taken on the largest and intermediate sides? - - -THE SOVEREIGNS OF ENGLAND. - -By the aid of the following, the order of the kings and queens of -England may be easily remembered:-- - - First William the Norman, then William, his son; - Henry, Stephen, and Henry, then Richard and John. - Next Henry the Third, Edwards, one, two, and three; - And again after Richard three Henrys we see. - Two Edwards, third Richard, if rightly I guess, - Two Henrys, sixth Edward, Queens Mary and Bess; - Then Jamie the Scot, then Charles, whom they slew; - Then followed Cromwell, another Charles, too. - Next James, called the Second, ascended the Throne, - Then William and Mary together came on. - Then Anne, four Georges, and fourth William past, - Succeeded Victoria, the youngest and last. - - -31. Take from 33 the fourth, fifth, and tenth parts of a certain -number, and the remainder is 0. What is the number? - - -A WALKING MATCH. - -32. T bets D he can walk 7 miles to his 6 for any time or distance; -so they agree to walk a certain distance, starting from opposite -points. T starts from point M to walk to N. D starts from N and walks -to M. They both started at the same moment, and met at a spot 10 -miles nearer to N than M. T arrives at N in 8 hours, and D arrives at -M in 12½ hours after meeting. Who wins the wager? How far from M -to N? And find the pace at which each walked? - - -THE ALPHABET. - -The total number of different combinations of the 26 letters of the -alphabet is 403291461126605635584000000. All the inhabitants on the -globe could not together, in a thousand million years, write out all -the combinations, supposing that each wrote 40 pages daily, each page -containing 40 different combinations of the letters. - - -“10 INTO 9 MUST GO.” - -[Illustration] - -33. - Ten weary footsore travellers, all in a woeful plight, - Sought shelter at a wayside inn one dark and stormy night. - - “Nine rooms-no more,” the landlord said, “have I to offer you; - To each of eight a single bed, but the ninth must serve for two.” - - A din arose; the troubled host could only scratch his head, - For of those tired men no two would occupy one bed. - - The puzzled host was soon at ease (he was a clever man), - And so, to please his guests, devised this most ingenious plan. - - -BOBBY (just from school)--“Mamma, I’ve got through the -promisecue-us examples, an’ I’m into dismal fractures.” - - -34. Find the expense of flooring a circular skating rink 30 feet -in diameter at 2s. 3d. per square foot, leaving in the centre a space -for a band kiosk in the shape of a regular hexagon, each side of which -measures 24 inches. - - -35. Gold can be hammered so thin that a grain will make 56 -square inches for leaf gilding. How many such leaves will make an -inch thick if the weight of a cubic foot of gold is 12 cwt. 95 lbs.? - - -School Inspector: “What part of speech is the word “am”? - -Smart Cockney Youth: “What? the ‘’am’ what you eat, sir, -or the ’am‘ what you is?” - - -MIND-READING WITH CARDS. - -Hand the pack (a full one) to be shuffled by as many spectators -as wish; then propose that someone takes the pack in his hand and -secretly chooses a card, not removing it, but noticing at what number -it stands counting from the bottom; he then returns the pack to you. - -Now you have to tell what number the card is from the top. You ask -any one of the spectators to choose any number between 40 and 50, and -whatever number is chosen the card will appear at that number in the -pack. Let us suppose the number chosen is 48. - -You then say that it is not necessary for you to even see the cards, -which will give you a good excuse for holding them under the table, -or behind your back. Now subtract the number chosen, 48, from 52, -which gives remainder 4, count off that many cards from the top, and -place them at the bottom. You next say to the gentleman who chooses -the card, that “it is now number 48, according to the general desire, -would you please let us know at what number it originally stood?” -Suppose he answers 7. Then, in order to save time, you commence -counting from the top at that number, dealing off the cards one by -one, calling the first card 7, the next 8, and so on. When you reach -48, it will be the card the gentleman had chosen. It is not necessary -to limit the choice of position to between 40 and 50, but it is -better for two reasons. - -First, that the number chosen be higher than that at which the card -first stood, also the higher the number chosen, the fewer cards are -there to slip from the top to the bottom. - - -36. Divide a St. George cross, by two straight cuts, into four -pieces, so that the pieces, when put together, will form a square. - -[Illustration] - - -PARSING. - -“What part of speech is ‘kiss’?” asked the High School teacher. - -“A conjunction,” replied one of the smart girls. - -“Wrong,” said the teacher, severely. “Next girl.” - -“A noun,” put in a demure maiden. - -“What kind of a noun?” continued the teacher. - -“Well--er--it is both common and proper,” answered the shy girl, and -she was promoted to the head of the class. - - -“QUICK.” - -TEACHER (to class)--“What is velocity?” - -BRIGHT YOUTH--“Velocity is what a person puts a hot plate -down with.” - - -OFFICE RULES. - - I. Gentlemen entering this Office will please - leave the door wide open. - - II. Those having no business will please call - often, remain as long as possible, take a chair, - make themselves comfortable, and gossip with the - Clerks. - - III. Gentlemen are requested to smoke, and - expectorate on the floor, especially during - Office Hours; Cigars and Newspapers supplied. - - IV. The Money in this Office is not intended for - business purposes--by no means--it is solely to - lend. Please note this. - - V. A Supply of Cash is always provided to Cash - Cheques for all comers, and relieve Bank Clerks - of their legitimate duties. Stamped cheque forms - given gratis. - - VI. Talk loud and whistle, especially when we - are engaged; if this has not the desired effect, - sing. - - VII. The Clerks receive visits from their - friends and their relatives; please don’t - interrupt them with business matters when so - engaged. - - VIII. Gentlemen will please examine our letters, - and jot down the Names and Addresses of our - Customers, particularly if they are in the same - profession. - - IX. As we are always glad to see old friends, it - will be particularly refreshing to receive visits - and renewal of orders from any former Customer - who has passed through the Bankruptcy Court, and - paid us not more than Sixpence in the Pound. A - WARM welcome may be relied on. - - X. Having no occupation for our Office Boy, he - is entirely at the service of callers. - - XI. Our Telephone is always at the disposal of - anyone desirous of using it. - - XII. The following are kept at this Office for Public Convenience:-- - A Stock of Umbrellas (silk), all the Local - Newspapers, Railway Time Tables, and other Guides - and Directories; also a supply of Note Paper, - Envelopes, and Stamps. - - XIII. Should you find our principals engaged, do - not hesitate to interrupt them. No business can - possibly be of greater importance than yours. - - XIV. If you have the opportunity of overhearing - any conversation, do not hesitate to listen. You - may gain information which may be useful in the - event of disputes arising. - - XV. In case you wish to inspect our premises, - kindly do so during wet weather, and carry your - umbrella with you. We admire the effect on - the floor; it gives an air of comfort to the - establishment. (The Umbrella Stand is only for - ornament, and on no account to be used). - -_P.S.--Our hours for listening to Commercial Travellers, Beggars, -Hawkers, and Advertising Men are all day. We attend to our Business -at Night only._ - - -A NEW WAY OF PUTTING IT. - - “Dirty days hath September, - April, June and November; - From January up to May, - The rain it raineth every day. - All the rest have thirty-one, - Without a blessed gleam of sun; - And if any of them had two and thirty, - They’d be just as wet and twice as dirty.” - - -Does the top of a carriage wheel move faster than the bottom? This -question seems absurd. That the top moves faster, however, is -perfectly correct; for if not it would simply move round in the same -place: in a wheel on a fixed axle the bottom moves backward as fast -as the top moves forward; but in a wheel that is going forward, -drawn by a progressive axle, the bottom does not go back at all, but -remains almost stationary until it is its turn to rise and go forward. - - -37. A General, arranging his army in a solid square, finds he has 284 -men to spare, but on increasing the sides of the square by one man, -he wants 25 men to complete the square. How many men has he? - - -“STEWING.” - -38. A student reads two lines more of “Virgil” each day than he did -the day before, and finds that, having read a certain quantity in -18 days, he will read at this rate the same quantity in the next 14 -days. How much will he read in the whole time? - - -39. Two bootmakers who lived in the town of B., thrown out of -employment, resolved to go to G., a town 24 miles north from B., -where there is a large factory; one of them went straight on to G., -but the other went first to C., a small township west of B., and then -went direct to G., his whole journey being 45 miles. What is the -distance from C. to G.? - - -40. A tree which grows each year 1 inch less than the previous year, -grew a yard in the first year; the value of the tree at any time is -equal to the number of pence in the cube of the number of yards of -its height. What is the value of the tree when done growing? - - -THIS OFTEN “STICKS” PEOPLE UP. - -41. What two odd numbers multiplied together make 7? - - -MAGIC SQUARES. - -A Magic Square is a series of figures arranged in the equal divisions -of a square in such a manner that the figures in each row when added -up, whether horizontally, vertically, or diagonally, form exactly the -same sum. - -They have been called “Magic” because the ancients ascribed to them -great virtues, and because this arrangement of numbers formed the -basis and principle of their talismans. Archimedes devoted a great -amount of attention to them, which has caused a great many to speak -of them as “the squares of Archimedes.” They may be either odd or -even. When the former, the following method will be found valuable:-- - -With the digits from 1 to 25 form a square so that the numbers when -added up horizontally, vertically, or diagonally will amount to 65. - -_Method._--Imagine an exterior line of squares above the magic square -you wish to form, and another on the right hand of it. These two -imaginary lines are shown in the diagram. - - - 18 25 2 9 - +----+----+----+----+----+ - | 17 | 24 | 1 | 8 | 15 | 17 - +----+----+----+----+----+ - | 23 | 5 | 7 | 14 | 16 | 23 - +----+----+----+----+----+ - | 4 | 6 | 13 | 20 | 22 | 4 - +----+----+----+----+----+ - | 10 | 12 | 19 | 21 | 3 | 10 - +----+----+----+----+----+ - | 11 | 18 | 25 | 2 | 9 | - +----+----+----+----+----+ - -1st. In placing the numbers in the square, we must go in the -ascending diagonal direction from left to right, any number which, by -pursuing this direction, would fall into the exterior line must be -carried along that line of squares, whether vertical or horizontal, -to the last square. Thus, 1 having been placed in the centre of the -top row, 2 would fall into the exterior square above the fourth -vertical line; then ascending diagonally 3 falls into the square -diagonally from 2, but 4 falls out of it to the end of a horizontal -line, and it must be carried along that line to the extreme left and -there placed. Resuming our diagonal ascension to the right we place 5 -where the reader sees it, and would place 6 in the middle of the top -row, but as we find 1 is already there we look for the direction to - -2nd. That when in ascending diagonally we come to a square already -occupied, we must place the number which, according to the 1st rule -should go into that occupied square directly under the last number -placed: thus, in ascending with 4, 5, 6, the 6 must be placed under -the 5, because the square next to 5 in diagonal direction is occupied. - - -A Promising Sign--I O U. - - -HOW TO FIND THE TOTAL OF A ROW OF FIGURES IN A MAGIC SQUARE. - -_Rule._--Multiply half the sum of the extremes by the square root of -the greatest extreme. - -Referring to the example given above, we see that the extremes 1 and -25 added equal 26--half of which is 13; this multiplied by 5 (the -square root of 25) gives 65 as the total for each row. - -Again, in the next question, the two extremes 1 and 81 equal 82, half -of this sum is 41, which multiplied by 9 (the square root of 81) -gives 369 as the total for each row. - - -42. Arrange the figures from 1 to 81 in a square that when added up -horizontally, vertically, or diagonally the sum will be 369. - - -HOW THEY WORKED IT. - -Mick and Pat, working in the country some distance from a hotel, -arranged with the landlord to take to their hut a small keg of rum. -They were unable to pay for the liquor at the time, having only one -threepenny piece between them; but Mick proposed that every time he -had a drink he would give Pat threepence, and Pat also agreed to -pay Mick for his drinks, the cash thus gathered to be brought to -the publican when the keg was empty. This proposal was accepted by -the publican, the keg of rum handed over to the two Irishmen, who -immediately started on their journey. They had not proceeded very far -before their burden made them thirsty. Mick is the first to pull up -with: “Hold on, Pat, I think I’ll have a drink.” “Begorra,” replied -Pat, “you’ll have to pay me for it then.” Mick hands the 3d. to Pat -before having a good “pull.” Pat now being the possessor of the price -of a drink, slakes his thirst by paying Mick 3d. for it. This form -of payment is kept up till the rum has disappeared. On their next -visit to the hotel, the 3d piece is handed to the landlord as being -payment, according to terms of agreement adopted by him. - - -43. Arrange the figure’s from 1 to 9 in a square, so that they will -add up to 15, horizontally, vertically, or diagonally. - -44. - -[Illustration: N.B.--Note this:] - -[Illustration] - - -45. A man sold a horse for £35 and half as much as he gave for it, -and gained thereby 10 guineas. What did he pay for the horse? - - -THE DISHONEST SERVANT. - -46. A gentleman having bought 28 bottles of wine, and suspecting his -servant of tampering with the contents of the wine cellar, caused -these bottles to be arranged in a bin in such a way as to count 9 -bottles on each side. Nothwithstanding this precaution, the servant -in two successive visits stole 8 bottles--4 each time--re-arranging -the bottles each time so that they still counted 9 on a side. How did -he do it? - - +-------------+ - | 2 5 2 | - | | - | | - | 5 5 | - | | - | | - | 2 5 2 | - +-------------+ - - -FATHER--“You are very backward in your arithmetic. When I was -your age I was doing cube roots.” - -BOY--“What’s them?” - -FATHER--“What! You don’t know what they are? My! my! that’s -terrible! There, give me your pencil. Now, we take, say, 28764289, -and find the cube root. First, you divide--no, you point off--no--let -me see?--um--yes--no--don’t stand there grinning like a Cheshire cat; -go upstairs and stay in your bedroom for an hour.” - - -A “TAKE-DOWN” WITH CARDS. - -This is a card trick which depends upon a certain “key,” the -possessor of which will always have the advantage over his -uninstructed adversary. It is played with the first six of each -suit--the four aces in one row, next row the deuces, threes, -fours, fives and sixes. The object now will be to turn down cards -alternately, and endeavour to make thirty-one points by so turning -without over-running that number. The chief point is to count so as -to end with the following numbers: 3, 10, 17 or 24. - -For instance, we will suppose it your privilege to commence the -count; you would commence with 3, and your adversary would add 6, -which would make 9; it would be then your policy to add 1 and make -10; then, no matter what number he adds he cannot prevent you making -17, which gives you the command of the trick. We will suppose he adds -6 and make 16; then you add 1 and make 17; then he to add 6 and make -23, you add 1 and make 24; then he cannot add any number to make 31, -as the highest number he can add is 6, which would only count 30, so -that you can easily add the remaining 1 and make 31. - -If your adversary is not wary, you may safely turn indifferent -numbers at the beginning, trusting to his ignorance to let you count -17 or 24; but, as his knowledge increases, he will soon learn that 24 -is a critical number, and to play for it accordingly. - -If both players know the trick, the first to play must be the winner, -as he is sure to begin with a 3, which commands the game. - - -ON AN OFFICE DOOR IN GOULBURN. - - A baptism in Hades’ depths, - As hot as boiling tar, - Awaits the man who quits this room - And leaves the door ajar. - But he who softly shuts the door - Shall dwell among the blest-- - Where the wicked cease from troubling - And the weary are at rest. - - -47. There are 5 eggs on a dish; divide them amongst 5 persons so that -each will get 1 egg and yet 1 still remain on the dish. - - -48. If a goose weighs 10 lbs. and a half of its own weight, what is -the weight of the goose? - - -THE GEOMETRICAL WONDER AND ARITHMETICAL ABSURDITY. - -Take a piece of cardboard 13 inches long and 5 wide, thus giving a -surface of 65 inches. Cut this strip diagonally, giving two pieces -in the shape of a triangle, and measure exactly 5 inches from the -larger end of each strip and cut in two pieces. Take these strips and -put them into the shape of an exact square, and it will appear to be -just 8 inches each way, or 64 inches--a loss of one square inch of -superficial measurement with no diminution of surface. - -[Illustration: 5 × 13 = 65 square inches.] - - -49. If we buy 20 sheep for 20 shillings, and give 2s. for wethers, -1s. 6d. for ewes, and 4d. for lambs, how many of each must we buy? - - -50. A sets out from a place and travels 5 miles an hour. B sets out -4½ hours after A and travels in the same direction 3 miles in the -first hour, 3½ miles the second hour, 4 miles the third hour, and -so on. In how many hours will B overtake A? - - -OFTEN ASKED. - -51. What is the difference between 4 square miles and 4 miles square? - - -TO TELL THE NUMBER THOUGHT OF ON A CLOCK. - -Ask a person to think of any number on the dial of a clock; you then -point, promiscuously at the various numbers, telling the person to -add the number of times you point to the number he thought of, and -when the total reaches 20, you will be pointing at the number he -selected. - -For instance, suppose he selected the number 5. You point -indifferently 7 times at the various numbers, but the 8th time your -pointer must be at XII., his addition will then be 13 (for 5 and 8 -added equal 13), the next at XI., his addition then 14, next at X., -and so on. When he calls 20, you will be pointing at the number he -thought of--5. - -[Illustration] - - -A very amusing experiment is to ask a person to write down the -figures around the dial of a clock. Nearly all know that the figures -are generally the Roman numerals; but, in writing them down, when -they come to the four, it is very often written IV. instead of IIII. - -It is said that a certain king, being unable to find any other fault -in a clock that had been constructed for him, declared that the -figure four should be represented by four strokes (IIII) instead -of IV. In vain did the clock-maker point out the mistake, for his -majesty adhered obstinately to his own opinion, and angrily ordered -the alteration to be made. This was done, and the precedent thus -formed has been followed by clockmakers ever since. - - -52. At dinner table: one great grandfather, 2 grandfathers, 1 -grandmother, 3 fathers, 2 mothers, 4 children, 3 grandchildren, -1 great grandchild, 3 sisters, 1 brother, 2 husbands, 2 wives, 1 -mother-in-law, 1 father-in-law, 2 brothers-in-law, 3 sisters-in-law, -2 uncles, 3 aunts, 1 nephew, 2 nieces, and 2 cousins. How many -persons? - - - “Can February March?” he asked. - “No, but April May,” was the reply. - “Look here, old man, you are out of June.” - “Don’t July about it.” - “It is not often one gets the better of your August personage.” - “Ha! now you have me Noctober.” - And then there was work for the coroner. - - -PANCAKE DAY. - -53. On Shrove Tuesday last, I’ll tell you what pass’d - In a neighbouring gentleman’s kitchen, - Where pancakes were making, with eggs, and with bacon - As good as e’er cut off a flitchen. - The cook-maid she makes four lusty pancakes - For William her favourite gardener, - “Pray be quick with that four,” cries Jack, “and make more, - For William won’t let me go partner.” - Being sparing of lard, the pan’s bottom she marr’d - In making the last of Will’s four; - So she said, “Pr’ythee, John, run and borrow a pan, - Or else I can’t make any more.” - Jack soon got a pan, but found by his span - That the first was more wide than the latter, - This being a foot o’er, whereas that before - Was three inches more and a quarter. - Jack cries, “Don’t me cozen, but make half a dozen. - For the pan is much less than before;” - Says Will, “For a crown (and I’ll put the cash down) - Your six will be more than my four.” - “Tis done,” says brisk Jack, and his crown he did stake, - So both of them sent for a gauger; - The dimensions he takes, of all their pancakes, - To determine this important wager. - He found, by his stick, they were equally thick, - So one of Will’s cakes he did take, - Which he straight cut in twain, twelve one-fifth[1] the chord line; - And gave the less piece unto Jack. - “To the best of my skill,” says the gauger, “this will - Make both of your shares equal and true;” - Will swore that he lied, so, the point to decide, - They refer themselves, sirs, unto you; - Then pray give your answers, as soon as you can, sirs, - For what with their quarrels and jars, - We’re afraid of some murder, for no day goes over - But they fight, and are cover’d with scars! - -[Illustration] - -[Illustration] - -[Illustration] - -[Illustration] - -[1] Inches. - - -A Great Prophet--100 per cent. - - - - -Interesting Items About the Almanac. - - -The reason why February has only 28 days, while the other months have -30 and 31 is attributable to the vanity of the Emperor Augustus. -His uncle and predecessor corrected the calendar, arranging the -year almost as we have it now; he gave to the year 12 months, or -365¼ days. The months were--March (the first month), April, May, -June, Quintilis, Sextiles, September, October, November, December, -January, and February (the latter being the last month of the year, -which among the Romans had consisted originally of 10 months). Cæsar -ordered that the year should begin with January, and divided the -days among them thus: January, March, May, Quintilis, September, -and November each had 31 days; April, June, Sextiles, October and -December had 30 days each; and February (the last month added to the -year) had 29 days regularly and a 30th day every fourth year. After -Julius Cæsar’s death, Mark Antony changed the name of Quintilis to -July as we have it now. Augustus wanted a month for himself, and -wanted it as long as his uncle’s month, so he took Sextiles for his -and changed the name to August. Then he took February’s 29th day and -added it to August, so that it might have 31 days; and, to avoid -having 3 months of 31 days each in succession, September and November -were reduced to 30 days, and October and December increased to 31 -days each. - - -Previous to the year 1752, the legal year in England commenced on -the 25th March. In that year it was enacted that the legal year -should begin on 1st January. The change brought the calendar into -unison with the actual state of the solar year. It is curious that -in Scotland the change which made the legal year begin on January -1st was effected in 1600. For some time after the change in England, -legal documents contained two dates for the period intervening -between 1st January and 25th March--that of the old year and that of -the new. - - -During the time of Oliver Cromwell, Christmas Day was described as a -superstitious festival, and put down in England by the strong hand of -the law. - - -There has been a superstitious notion that Fools’ Day dated back to -the time of Noah’s Ark. The dove that was sent forth from the Ark is -supposed to have returned on April 1st. - - -THE MOST REMARKABLE MONTH was February, 1866. It had no full -moon. January had two full moons, and so had March, but February had -none. This had not occurred since the creation of the world, and it -will not occur again, so scientists tell us. - -_All Fools’ Day_ had it’s origin in France, before the time of the -Reformed Calendar. When the year commenced on March 25th, the French -frequently paid their New Year’s visits and bestowed their gifts on -April 1st, as March 25th occurred in Passion Week. After the adoption -of the new calendar, however, these New Year’s observances took place -on January 1st, and it was a common thing for people to forget the -change of date. Pretended presents and mock ceremonial visits became -common, and the persons thus imposed on were known as April fish, -_i.e._, a mackerel, which, like a fool, is easily caught. Hence, -All Fools’ Day. - - -54. Being at the summit of a tower 400 ft. high, I dropped a cricket -ball from my hand, causing it to alight on a ledge 260 ft. from the -base, over which it rolled and fell to the earth: supposing that -1½ seconds were occupied by the rolling of the ball over the -ledge, how many seconds elapsed from the ball leaving my hand till it -touched the earth, and what was the acquired velocity at the moment -of contact? - - -PRACTICAL ILLUSTRATION. - -In one of our great public schools a master known to successive -generations of his pupils for fifty years as “old Buggus” delighted -in surprising his boys with strange sayings and doings. On one -occasion, desirous of illustrating a question in the arithmetic -lesson, he said to a boy, “I am a tripe merchant, and this platform -is my shop. You will come here and buy a pound of tripe. Now, begin.” - -[Illustration] - -“Please, I want a pound of tripe,” said a boy, sauntering up. -“Where’s your money?” demanded old Buggus, hoping to put the boy out -of countenance. - -“Where’s your tripe?” was the ready retort; but it gained for its -unfortunate author four hours’ detention on the next holiday. - - -55. A syphon would empty a cistern in 48 minutes, a tap would fill it -in 36. How long will it take to fill the cistern when both taps are -in action? - - -Born to rule--a book-keeper. - - -“MORE HASTE LESS SPEED.” - -56. A compositor, hurrying whilst setting up type for an arithmetic -book--“How to Become Quick at Figures”--accidentally dropped the work -of a problem; unfortunately he mislaid the copy, and all that he -remembered was that both multiplicand and multiplier consisted of two -figures. The scattered type represented the following figures:--1, 2, -3, 3, 4, 6, 7, 8, 8, 9, 9. With the aid of a pencil and a piece of -paper the compositor managed after a while to rearrange the figures -in their proper place. What was the problem? - -[Illustration] - - -PROFITABLE CARELESSNESS. - -A very amusing story is told of a harness-maker who lived some years -ago in London. He had a handsome saddle in his shop, occupying a -conspicuous position therein. On his return from luncheon one day he -observed that the saddle was gone. Calling to his foreman, he said: - -“John, who has bought the saddle?” - -“I’m sure I don’t know, sir,” said the foreman, scratching his head -as if he were trying to think. “I cannot tell, and the worst part of -it is, it hasn’t been paid for. While I was at work in the back of -the shop a gentleman came in, priced it, decided to take it, told -me to charge it, and throwing it into his trap, drove off, before I -could think to ask his name.” - -“That was very stupid of you,” said the harness-maker, disposed to be -angry at the man’s carelessness. “Very likely we have been robbed.” - -“I don’t think that sir,” said the foreman, “for I’m very sure that -the gentleman has traded here before.” - -“Well, I can’t afford to lose the money,” said the harness-maker. -“We’ll have to find out who took it and send him the bill. Ah!” he -added, with a smile, after a moment’s reflection, “I have it. We’ll -charge it up to the account of every one of our customers who keep -open accounts here. Those who didn’t get it will refuse to pay, so we -shall be all right.” - -“The book-keeper was instructed to do this, and the bills in due -course of time went out. Some weeks later the harness-maker asked the -book-keeper if he had succeeded in discovering who the customer was. - -“No, sir,” he replied, “and we never shall, I fear, sir, for about 40 -people have paid for it already without saying a word.” - - -A CYCLE CATCH. - -Tie a cord to the pedal of a bicycle, such pedal to be the one that -is the nearer to the ground, and, standing behind the back wheel, -pull the cord, when, strange as it appears, the machine will come -towards you, although everyone would first imagine that the bicycle -would move forward. How is this? - -[Illustration] - - -One ought to have dates at one’s finger ends seeing they grow upon -the palms. - - -TO TELL THE SPOTS ON THE BOTTOM CARDS OF SIX HEAPS. - -Allow anyone to choose six cards from a full pack. Tell him the -court cards count 10, and the other cards according to their pips. -Having made his selection, tell him to lay the chosen cards upon the -table face downwards, without allowing you to see them, and to place -upon each as many cards as pips are required to make 12. Whilst he -is doing so, you should be out of the room or blindfolded. On your -return he hands you the cards left over, and you have to tell the -total number of spots on the six bottom cards. - -Suppose he had chosen 10, 6, 1, K, 3 and 7, which totals 37, now -on the 10, he would place two cards to make 12; on the 6, he would -place 6; and on the 1, 11 would be placed, and so on. On receiving -the remaining cards from him you pretend to be looking through them -carefully, but you simply want to know how many he has given you, -which in the above example would be 11. To this number you add 26, -which gives 37, the total spots required. - -Should there not be enough cards left on hand to complete the six -heaps, you can ask him how many cards he is short of, and this -number, subtracted from 25, will give the total. It is better not to -allow the person to choose six cards right off at the beginning, but -for him to shuffle and cut the pack as he pleases, and to take the -cards as they come. - - -BOOK-KEEPING COMMANDMENTS. - -By _Ledger_ laws, what I receive Is _Debtor_ made to those who -give. _Stock_ for my debts must Debtor be, and Creditor by Property. -_Profit and Loss_ accounts are plain, I Debit loss and Credit gain. - - -57. How far does a man walk while planting a field of corn 285 feet -square, the rows being 3 ft apart from the fence? - - -A MATTER OF OPINION. - -A man walks round a pole on the top of which is a monkey. As the man -moves, the monkey turns on the top of the pole, so as still to keep -face to face with the man. Now, when the man has gone round the pole, -has he or has he not gone round the monkey? - -[Illustration] - - -TRY IT. - -Take the number 15, multiply it by itself, and you have 225; now -multiply 225 by itself, then multiply that product by itself, and -so on until 15 products have been multiplied by themselves in turn. -The final product called for contains 38,539 figures (the first of -which is 1412). Allowing three figures to an inch, the answer would -be over 1070 feet long. To perform the operation would require about -50,000,000 figures. If they can be made at the rate of 100 a minute, -a person working 10 hours a day for 300 days in each year would be 28 -years on the job. - - -PATHETIC ADVERTISING. - -“Died, on the 11th ultimo., at his shop in Fleet-street, Mr. Edward -Jones much regretted by all who knew and dealt with him. As a man, -he was amiable; as a hatter, upright and moderate. His virtues were -beyond all price, and his beaver hats were only £1 4s each. He has -left a widow to deplore his loss, and a large stock to be sold cheap -for the benefit of his family. He was snatched to the other world in -the prime of life, and just as he had concluded an extensive purchase -of felt, which he got so cheap that the widow can supply hats at -a more moderate charge than any house in London. His disconsolate -family will carry on his business with punctuality.” - - -58. In one corner of a hexagonal grass paddock each of the sides of -which is 40 yards long, a horse is tethered with a rope 50 yards -long. How many square yards can he graze over? - - -59. A and B start together from the same point on a circular path, -and walk till they both arrive together at the starting point. If A -performs the circuit in 224 seconds and B in 364 seconds, how many -times do they each walk round? - - -“IF.” - -If you could sell the sea at 1d. per 10,000 gallons, it would bring -in 155 billion pounds. If you were to try and pump it dry, at the -rate of 1,000 gallons per second, it would take 12,000 million years. -There is always an “if” in these things! - -60. A lady met a gentleman in the street. The gentleman said “I think -I know you.” The lady said he ought, as his mother was her mother’s -only daughter. What relation was he? - -[Illustration] - - -A CRICKET “CATCH.” - -61. In an eleven, when the ninth batsman goes in, how many wickets -have to fall before all are out? - - -62. A boat’s crew can row eight miles an hour in still water; what -is the speed of a river’s current if it takes them 2 hours and 40 -minutes to row 8 miles up and 8 miles down? - - -BAD WRITING. - -In a well-known firm in Sydney the clerks are presided over by a -rather impetuous manager, whose violent fits of temper very often -dominate his reason. For instance, the other day he was wiring into -one of them about his bad work. - -“Look here, Jones,” he thundered, “this won’t do. These figures are a -perfect disgrace to a clerk! I could get an office boy to make better -figures than those, and I tell you I won’t have it! Now, look at that -five, it looks just like a three. What do you mean, sir, by making -such beastly figures? Explain!” - -“I--er beg your pardon, sir,” suggested the trembling clerk, his -heart fluttering terribly, “but--er well, you see, sir, it is three.” - -“A three?” roared the manager; “why, it looks just like a five!” - - -63. Write 24 with three equal figures, neither of them being 8. - - -THE WRONG COLUMN. - -64. A clerk, while posting from day book to ledger, transposed an -amount by placing the pence in the shilling column and the shillings -in the pence column, thereby causing an error of 9s. 2d. With what -amount could he make such a mistake? - - -EDUCATIONAL VAGARIES. - -_Extracts from Reports of Country Provisional Schools._ - -School No. 1: On roll, 1 boy, 1 girl; total, 2. Average attendance, -0·6 boy, 0·6 girl; total, 1·2. - -School No. 2: On roll, 2 boys, 2 girls; total 4. Average attendance, -1·6 boys, 1·3 girls; total, 2·9. - -School No. 3: On roll, 2 boys, no girls. Average attendance, 0·8 boys. - -By the above we see the public are paying for a teacher to provide -education for eight-tenths of a boy! - - -65. - Three-fourths of a cross, and a circle complete, - Two semi-circles at a perpendicular meet; - Next add a triangle which stands on two feet, - Two semi-circles and a circle complete. - - -A DISPUTE. - -66. Two men have an equal interest in a grindstone, which is 5 ft. -6 in. in diameter. The centre of the stone, to the extent of a -diameter of 18 in., is useless, and not to be taken into account. - -Required to find the depth to which the first partner may be allowed -to grind away from the stone in order to leave an equal share of the -stone to the second partner. - -[Illustration] - - -BANK NOTE VERSE. - -On the backs of bank notes one sometimes meets with strange -and peculiar sentiments. “Go, poor devil, get thee gone,” is the -kind of parting salutation most in favour; but the following is chiefly -notable as a rare instance of the bank-note rhymester parting with -his money in a Christian spirit: - - Farewell, my note, and wheresoe’er ye wend, - Shun gaudy scenes, and be the poor man’s friend; - You’ve left a poor one--go to one as poor; - And drive despair and hunger from his door. - - -An Irish merchant, who felt annoyed at a complaining letter he -received from a customer, wrote back:--“We decline to acknowledge the -receipt of yours of the 15th.” - - -If to-day is the to-morrow of yesterday, is to-day the yesterday of -to-morrow? - -67. Suppose that four poor men build their houses around a pond, and -that afterwards four evil-disposed rich men build houses at the back -of the poor people--as shown in illustration--and wish to have a -monopoly of the water: how can they erect a fence so as to shut the -poor people off from the pond? - -[Illustration] - - -SOME TRADE SIGNS AND MOTTOES. - -Many curious inscriptions are to be found displayed on shop windows, -office doors, etc. - -Here are a few:-- - -A Pawnbroker.--“Mine is a business of the greatest interest.” - -A Flourishing Bootmaker.--“Don’t you wish you were in my shoes?” - -A Publican.--“Good beer sold here, but don’t take my word for it.” - -A Hairdresser.--“Two heads are better than one.” - -A Carter.--“Excelsior--hire and hire.” - -A Baker.--“The staff of life I do supply, by it you live and so must I.” - -A Butcher.--“We kill to dress, not dress to kill.” - -A Builder.--“I send innocent men to the ‘scaffold.’” - -A Clerk.--“I possess more pens than pounds.” - -A Dentist.--“I look ‘down in the mouth’ and am happy.” - -A Doctor.--“I take pains to remove pains.” - -A Hatter.--“I shelter ‘the heir apparent’ and protect ‘the crown.’“ - -A Photographer.--“Mine is a developing business and mounting rapidly.” - -A Solicitor.--“I study the law--and the profits.” - -An Undertaker.--“No complaints from our customers.” - - -RIVAL BUTCHERS. - -T. JONES.--“Sausages, 3d. per lb.--to pay more is to be -robbed.” - -J. SMITH.--“Sausages, 4d. per lb.--to pay less is to be -poisoned.” - - -A French confectioner, proud of his English, and wishing to let his -customers know that their wants would be attended to without delay, -put out the notice, “Short weights here.” - -A shopkeeper in the old country had printed under his name “The -little rascal.” When asked the meaning of this strange sign, he -replied, “It distinguishes me from the rest of my trade, who are all -great rascals.” - - -On an Office Door.--“Shut this door, and as soon as you have done -talking on business, serve your mouth the same way.” - - -“SHE.” - -68. - A country spark addressed a charming “she,” - In whom all lovely features did agree; - But being void of numbers, as doth show, - Desirous was the lady’s age to know. - “My age is such that if multiplied by three, - Two-sevenths of the product triple be: - The square root of two-ninths of that is four;-- - Tell me my age or never see me more.” - -[Illustration] - - -RUNNING SHORT. - -69. A vessel on a 3 months’ trip has provisions for 4 months, but -the stores are served out as if the voyage had to be completed in 3 -months. At the end of 2 months, it is discovered that the voyage will -take 3½ months. To what proportion must the rations be reduced for -the remaining time? - - -In a certain town in the North of Queensland, a class of young -men was formed to receive lessons in short methods of business -arithmetic. The teacher was endeavouring to knock into the head of -a young man that the cost of a dozen articles is the same number of -shillings that a single article costs in pence. To illustrate the -rule, he gave the following example:-- - -“If I buy 1 dozen apples at 1d each, then the dozen will cost 1 -shilling; and if I buy 1 dozen oranges at 2 pence each, the dozen -will cost 2 shillings. Now, supposing I buy 1 dozen at 3 pence each, -how much will the dozen cost?” - -YOUNG MAN (after two minutes’ reflection)--“Are they apples -or oranges?” - - -A DRAUGHTS PUZZLE. - -70. Ten draughtsmen are placed in a row. The puzzle is to lift one up -and passing over two at a time (neither more nor less) to place it on -the top, or to “crown” the next one, continuing in this fashion until -all are crowned. In passing over a piece already crowned, it is to be -reckoned as two pieces. - - -71. In the centre of a pond 20 feet square there is a small island, -on which is growing a tree. Two boys notice there is a bird’s nest -on the top of the tree, but the difficulty is to reach the island, -as they have 2 short planks that only measure 8 feet each. After a -little while they hit on an ingenious plan, and, without nailing the -planks together, manage to place them so they can reach the tree in -safety. How did they do it? - - -TEACHER--“Now, I want all the children to look at Tommy’s -hands, and see how clean they are, and see if all of you cannot come -to school with cleaner hands. Tommy, perhaps, will tell us how he -keeps them so nice?” - -TOMMY--“Yes ’m; mother makes me wash the breakfast things -every morning.” - - -BRAIN-BEWILDERERS. - -An amusing periodical got up by the boys of a certain college gives a -capital skit on the style of examination-papers frequently presented -for the torture of pupils. Here are a few examples:-- - -Supposing the River Murray to be three cubits in breadth--which -it isn’t--what is the average height of the Alps, stocks being at -nineteen and a-half? - -If in autumn apples cost fourpence per pound in Melbourne, and -potatoes a shilling a score in spring, when will greengages be sold -in Brisbane at three-halfpence each, Sydney oranges being at a -discount of five per cent.? - -If two men can kill twelve kangaroos in going up the right side of a -rectangular turnip-field, how many would be killed by five men and a -terrier pup in going down the other side? - -If a milkmaid four feet ten inches in height, while sitting on a -three-legged stool, took four pints of milk out of every fifteen -cows, what was the size of the field in which the animals grazed, and -what was the girl’s name, age, and the occupation of her grandfather? - -If thirty thousand millions of human beings have lived since the -beginning of the world, how many may we safely say will die before -the end of it? N.B.--This example to be worked out by simple -subtraction, algebra, and the rule of three. Compare results. - - -72. Find two numbers in the proportion of 9 to 7 such as the square -of their sum shall be equal to the cube of their difference. - - - - -ARITHMETICAL THOUGHT READING. - - -A great deal of fun can be derived from puzzles of this nature--they -are endless in variety--and as they depend upon some principle in -arithmetic should be easily remembered. - -Example 1. - Think of a number, say 5 - Double it 10 - Add 5 15 - Add 12 27 - Take away 3 24 - Halve it 12 - Take away number first thought of--5 - The answer will _always_ be 7 - - -Example 2. - Think of a number, say 8 - Square it 64 - Subtract the square of the number which is - 1 less than the number thought of--that - is 7--whose square is 49--leaves 15 - Add 1 16 - -When this last number is told, halve it, and you will arrive at -the original number--8. - - -Example 3. - Think of a number, say 9 - Multiply by 3 27 - Add 2 29 - Multiply by 3 87 - Add 2 more than the number thought of (11) 98 - -The number of _tens_ in the last answer gives the number thought -of, viz., 9. - - -Example 4. - Think of a number, say 7 - Multiply by 3 21 - [If product be odd] add 1 22 - Halve it 11 - Multiply by 3 33 - [If product be odd] add 1 34 - Halve it 17 - -Ask how many 9’s are in the remainder, when, of course, the reply -will be 1. - -The secret is to bear in mind whether the first sum be odd or even. -If odd first time, retain 1 in the memory; if odd a second time, 2 -more, making 3; to which add 4 for every 9 contained in the remainder. - -In the above example, there being only one 9 in 17, this gives us 4, -which added to 3 produces the number thought of--7. When even simply -add 4 for every 9 in remainder. - - -HOW TO TELL THE AGE OF A PERSON. - -Tell a person to write down the figure which represents the day of -the week on which he was born;--thus, 1 for Sunday, 2 for Monday, and -so on; next, the figure for the month--1 for January, 2 for February, -&c.; then the date of the month; now tell him to multiply the number -thus formed by 2, add 5, multiply by 50, and then to add his age, and -from this sum to subtract 365; now you ask him for the remainder, to -which you _secretly_ add 115. - -The result will be:--The first figure, the day of the week; the next, -the month in the year; the next, the date of the month; and the last, -the age in years. - -Example: - -A person was born on Wednesday, 11th June, 1863. - - Write 4, as Wednesday is 4th day of the week. - " 6, as June is 6th month of year. - " 11, as that is the date given, 11th June. - - The figures then are-- 4611 - 2 - ---- - 9222 - 5 - ---- - 9227 - 50 - ------ - 461350 - 35 Age - ------ - 461385 - 365 - ------ - 461020 - 115 - -------- - 4-6-11-35 - - -A GOOD FIGURE TRICK. - -Tell a person to set down a sum of money less than £12, in which -the pounds exceed the pence; next to reverse this amount, making -pence pounds, etc., and to subtract the one from the other, then -set beneath the result itself reversed, adding the last two lines -together, when you will tell him the result, which will _always_ -be £12 18s. 11d. - - Example: £10 8 7 - 7 8 10 - -------- - 2 19 9 - 9 19 2 - -------- - £12 18 11 - -If the performer be blindfolded the trick looks very mystifying; -he should not, however, repeat it, for many would soon discover -the secret, but as the peculiarity is not confined to money, other -illustrations can be given if required--for instance--if a number of -yds., ft. and inches (less than 12 yds.) be operated on, the final -answer will always be 12 yds. 1 ft. 11 inches; and if a number of -cwts., qrs. and lbs. (less than 28 cwts.) be chosen, the answer will -always be 28 cwts. 2 qrs. 27 lbs. - - -“Girls” and “Boys.” - -At a school examination, the inspector set the girls to write an -essay on “Boys” and the boys to write one on “Girls.” - -The following was handed in by a girl of 12:-- - -“The boy is not an animal, yet they can be heard to a considerable -distance. When a boy hollers he opens his big mouth like frogs, but -girls hold their tongues till they are spoken to, and then they -answer respectable, and tell just how it was. A boy thinks himself -clever because he can wade where it is deep, but God made the dry -land for every living thing, and rested on the seventh day. When the -boy grows up he is called a husband, and then he stops wading and -stays out at nights, but the grew up girl is a widow and keeps house.” - -One of the boys sent in:-- - -“Girls are very stuck up and dignified in their manners and -behaveyour. They make fun of boys, and then turn round and love them. -Girls are the only people that have their own way every time. Girls -is of several thousand kinds, and sometimes one girl can be like -several 1000 girls if she wants anything. I don’t beleive they ever -killed a cat or anything. They look out every nite and say, “Oh, -ain’t the moon lovely!” Thir is one thing I have not told, and that -is they always now their lessons bettern boys. This is all I now -about girls, and father says the less I now the better for me.” - - -73. The sum of the squares of two consecutive numbers is 1105. -What are the numbers? - - -A PROBLEM FOR PLUMBERS. - -74. A requires a tank in size capable of holding the quantity of -water that would be caught from the roof of his house in a fall of -3 inches of rain. The roof (commonly called a “hip-roof”) is at an -angle of 45 degrees to the wall plates. The length of house is 30 ft., -breadth 24 ft., and length of ridge to roof 6 ft. But the eaves of -the iron used for the roofing were so large as to increase its (the -roof’s) dimensions by 3 inches all round, and the spouting added -another 3 inches all round. Find the number of gallons the tank would -require to contain; also dimensions of tank to be made so that its -height must exceed its diameter by no more than 12 inches? - - -“The ’embers of a dying year”--November, December. - - -TO TELL THE COMPASS BY A WATCH. - -Hold the watch face-downwards above your head with the hour hand -pointing towards the sun, and half-way between the hour hand and the -figure XII will be the North. - - -75. Divide 100 into two parts, so that a quarter of one exceeds -one-third of the other by 11. - - -STRANGE BUT TRUE. - -76. Two persons were born at the same place at the same moment of -time; after an age of 50 years they both died also at the same place -and at the same instant, yet one had lived 100 days more than the -other. How was this remarkable event achieved? - - -ASTRONOMICAL. - -77. The planet Jupiter is five times further from the sun than our -earth, and 1331 times larger. Assuming that the diameter of the earth -is 7912 miles, find Jupiter’s diameter, circumference and area. - - -AN UNSOLVED PROBLEM. - -One of the commercial questions of the day which remains to this time -unsettled, is whether the fact of a gentleman having NO TIN may not -have something to do with the answer he invariably sends of NOT IN -when anyone calls on him with a bill. - - -78. Find nine numbers in arithmetical progression--common difference -3--whose sum is equal to 5670, and arrange in a square, each side -containing three different numbers, so that, when added vertically, -horizontally or diagonally, the sum of each three numbers will amount -to 1890. - - -79. I have a box. The pieces forming the sides are 5 ft long, and -those forming the ends are 4 ft. broad. The box, when measured -externally all round, measures 18 ft 4 in., and when measured all round -internally, measures 17 ft 8 in. How can this be? - -[Illustration] - - -Teacher: “Who was it that supported the world on his shoulders?” -Bright Pupil: “It was Atlas, ma’am.” Teacher: “And who supported -Atlas?” Bright Pupil: “The book don’t say, but I s’pose it was his -wife.” - - -ON BOTH SIDES OF A DOOR IN A MELBOURNE OFFICE. - -THE MAN WHO FORGETS THE DOOR. - - Oh, there’s an individual who ev’rywhere abounds, - Thro’ trains and shops and offices he makes his busy rounds, - And in and out for ever he is going o’er and o’er, - To keep somebody after him attending to the door! - - In sultry summer, when to catch a cooling breeze we’ve tried, - And carefully have opened every door and window wide, - ’Tis then you may be certain as he vanishes from sight, - He’ll die but that he’ll shut the door--and close it very tight! - - But when the winds of winter come, with cold and biting breath, - Oh, then it is the awful wretch is tickled ’most to death! - His sense of pleasure reaches to a point that is sublime; - He never fails to leave the door wide open every time! - - -80. A man agrees to work for £8 a year and a suit of clothes. He left -at the end of seven months, and received £2 13s. 4d. and his clothes. -What is the value of the suit? - - -81. A bought four horses for £120. For the second he gave £3 more -than for the first, for the third £2 more than for the second, and -for the fourth £6 more than the third. Find price of each. - - -82. With eight pieces of card of the shape of figure A, four of -figure B and four of figure C, and of proportionate sizes, form a -perfect square. - -[Illustration] - - -83. Place four 5’s so that they shall express 6½. - - -“SHE” AGAIN. - -84. - The country spark that asked the charming “she” - How many years of age that she might be, - Again asked her to tell to him in haste - How many inches she was round the waist. - “My waist is such if multiplied by four, - Four-fifths of product add on my age more, - The square root of three-fifths of this is six: - Now find my waist, and get out of this fix.” - - -SOME LONG WORDS. - -The eight longest words in the language are philoprogenitiveness, -incomprehensibleness, disproportionableness, transubstantiationalist, -suticonstitutionalist, honourifibilitudinity, velocipedestrianistical, -and proautionsubstantionist. The last four are not found in the best -dictionaries, but that most hideous word, -“Dacryocystosyringokatakleisis,” is in some of the new lexicons. - - -HIS OWN GRANDFATHER. - -The complication of relationship brought about by marriage is the -cause of many a family squabble, but it is seldom one hears of fatal -results attending such matters. According to an American newspaper, -a resident of Pennsylvania committed suicide a few days ago from a -melancholy conviction that he was his own grandfather. - -The following is a copy of a singular letter he left:--“I married a -widow who had a grown-up daughter. My father visited our house very -often, fell in love with my step-daughter, and married her. So my -father became my son-in-law and my step-daughter my mother, because -she was my father’s wife. Some time afterwards my wife had a son; he -was my father’s brother-in-law and my uncle, for he was the brother -of my step-mother. My father’s wife--_i.e._, my step-daughter--had -also a son; he was, of course, my brother, and in the meantime -my grandchild, for he was the son of my daughter. My wife was my -grandmother, because she was my mother’s mother. I was my wife’s -husband and grandchild at the same time. And as the husband of a -person’s grandmother is his grandfather, I was my own grandfather.” -Thus he died, a martyr to his own existence. - -[Illustration] - -85. If 100 stones are placed on the ground, in a straight line, at -the distance of 1 yard from each other, how far will a person travel -who will bring them all, one by one, to a basket placed one yard from -the first stone? - - -A little boy, writing a composition on the zebra, was requested to -describe the animal and to mention what it was useful for. After deep -reflection, he wrote:--“The zebra is like a horse, only striped. It -is chiefly useful to illustrate the letter Z.” - - -86. I bought a horse and sold him again at 5 per cent. on my -purchase; now, if I had given 5 per cent. less for the horse, and -sold him for 1s. less, I would have gained 10 per cent. What was the -original cost? - - -87. Find three numbers such that the first with half of the other -two, the second with one-third of the other two, and the third with -one-fourth of the other two, shall be equal to 34? - - -THE FAMOUS “45” PUZZLE. - -88. Take 45 from 45, and leave 45 as a remainder. There are at least -two ways of doing this. - -89. How can 45 be divided into 4 such parts that if you add 2 to the -first part, subtract 2 from the second part, multiply the third part -by 2, and divide the fourth part by 2, the sum of the addition, the -remainder of the subtraction, the product of the multiplication, and -the quotient of the division are equal? - -90. The square of 45 is 2025, if we halve this we get 20/25 and -20 plus 25 equals 45. Find two other numbers of four figures that -produce the same peculiarity. - - -91. A mother of a family being asked how many children she had, -replied: “The joint ages of my husband and myself are at present six -times the united ages of our children; two years ago their united -ages were ten times less than ours, and in six years hence our joint -ages will be three times theirs.” How many children had she? - - -WHERE THE CREEDS AGREE. - -The Mahometans, Christians and Jews, with different creeds, are all -striving to reach the same place--Heaven. Now, we will endeavour to -show, by figures, that it is possible for them all to accomplish -their purpose. - -The figures 4, 5, 6, at the angles of the large triangle, represent -respectively the above mentioned sects. They are very distant from -each other, but we will induce them to meet half-way. Thus, the -Mahometans and Jews meet at 10, the Mahometans and Christians at 9, -and the Jews and Christians at 11; and by joining these totals to -the opposite numbers we see they all meet at last in Heaven (15). -It should be mentioned that any numbers whatever may be used to -represent the sects, but the result will always be the same. - -[Illustration] - - -“SHE” ONCE MORE. - -92. The country spark again addressed the charming “she.” This time -he wished to know her height. She replied, “My height (in inches) if -divided by the product of its digits, gives as quotient 2, and the -digits are inverted by adding 27.” - -“You have a bright look, my boy,” said the visitor at the school. -“Yes, sir,” replied the candid youth; “that’s because I forgot to -rinse the soap off my face this morning.” - - -HIS LAST WILL AND TESTAMENT. - -93. A father on his death-bed gave orders in his will that if his -wife, who was then pregnant, brought forth a son, he should inherit -two-thirds of his property, and the mother the remainder; but if she -brought forth a daughter the latter should have only one-third, and -the mother two-thirds. The widow, however, was delivered of twins,--a -boy and a girl. What share ought each to have of the property left -by the father, who had his life insured in the Australian Mutual -Provident Society for £7,000. - -[Illustration] - - -94. - Money lent at 6 per cent - To those who choose to borrow; - How long before I’m worth a pound - If I lend a crown to-morrow? - - -A KEEN EYE TO BUSINESS. - -Upon the death of the senior partner of an Australian firm a notice -of the sad event was sent to, amongst others, a German lithographic -establishment. The clerk in this German house, who was instructed to -answer the communication, wrote the following letter of condolence:-- - -“We are greatly pained to hear of the loss sustained by your firm, -and extend to you our heartiest sympathy. We notice the circular you -sent us announcing Mr. S----’s death is lithographed by Messrs.----. -We regret that you did not see your way to let us estimate for the -printing of the same. The next time there is a bereavement in your -house we will be glad to quote you for the lithographic circulars, -and are confident that we can give you better work at less cost -than anybody else in the business. Trusting that we may soon have -an opportunity of quoting you our prices, we remain, with profound -sympathy, yours truly,----.” - - -An American journal, describing a new counterfeit bank-note, says the -vignette is “cattle and hogs, with a church far in the distance”--a -good illustration of the world. - -95. On a square piece of paper mark 12 circles as shown in diagram. -The puzzle is to divide the figure into four pieces of equal size, -each piece to be of the same shape, and to contain three circles, -without getting into any of them. - -[Illustration] - - -THE ORIGIN OF THE “STONE.” - -Measurement of weight by the “stone” arose from the old custom -farmers had of weighing wool with a stone. Every farmer kept a large -stone at his farm for this purpose. When a dealer came along he -balanced a plank on top of a wall, and put the stone on one end of it -and the bags of wool on the other, until the weights were equal. At -first the stones were of all sorts and sizes and weights, with the -result that dealers who wished to make a living had to be remarkably -knowing in their estimates of them. The many inconveniences involved -by this inequality resulted in all stones being made of a uniform -weight as far as wool was concerned. The weight of a stone of -potatoes, meat, glass, cheese, &c., all differ. - - -A little boy was reading in his Scottish history an account of the -battle of Bannockburn. He read as follows: “And when the English army -saw the new army on the hill behind, their spirits became damped.” - -The teacher asked him what was meant by “damping their spirits,” and -the boy, not comprehending the meaning, simply answered, “Putting -water in their whisky.” - - -THUNDER AND LIGHTNING CALCULATION. - -96. Between the earth and a thundercloud there are four currents of -air, having a temperature of 87, 57, 47, and 37 degrees respectively. -The first current is half the depth of the second, the second half -the third, and the third half the fourth. If a peal of thunder is -heard 2-3251/4256 seconds after the lightning flash, find the depth -of the fourth current and the time occupied by the sound in passing -through it. - - - 97. - First cut out, with a pen-knife, in paste-board or card, - The designs numbered 1, 2 and 3, - Four of each; after which, as the puzzle is hard, - You had better be guided by me - To a certain extent; for, in fixing, take care - That each portion is fitted in tight, - Or they will not produce such a neat little square - As they otherwise would if done right. - -[Illustration] - - -QUITE PROPER. - -“What is a propaganda,” inquired the teacher. The boy looked at the -ceiling, wrinkled his forehead, wrestled with the question a minute -or two, and then answered that it was the brother of a proper goose. - - -DECEMBER AND MAY. - -98. An old man married a young woman; their united ages amounted -to 100; the man’s age, multiplied by 4 and divided by 9 gives the -woman’s age. What were their respective ages? - - -99. A and B set out on a walking expedition at the same time--A from -Melbourne to Geelong, and B from Geelong to Melbourne. On reaching -Geelong A immediately starts again for Melbourne. Now, A arrives at -Geelong four hours after meeting B, but he reaches Melbourne three -hours after their second meeting. In what time did each perform the -journey? - - -100. What two numbers are those of which the square of the first plus -the second equals 11, and the square of the second plus the first -equals 7? - - -A schoolmaster, describing a money-lender, says, “He serves you in -the present tense, he lends you in the conditional mood, keeps you in -the subjunctive mood, and ruins you in the future.” - - -101. “How much money have I,” says a father to his son. Son -replied, “They don’t teach prophecy at our school.” “Well, they -teach arithmetic, I suppose,” rejoined the father, smartly; “if you -multiply one-half, one-third, one-fourth, one-sixth, three-quarters, -and two-thirds of my money together, the product will be 10368. Now -find out how many pence I have.” - - -102. A person has 1260 quarters of wheat. He sells one-fifth at a -gain of 5 per cent., one-third at a gain of 8 per cent., and the -remainder at a gain of 12 per cent. Had he sold the whole at a gain -of 10 per cent. he would have made £23 2s. more than he did. Find the -cost price of one quarter. - - -103. Is the word “with” ever used as a noun? - - -THE GREAT PUZZLE OF THE CENTURY. - -104. Place the nine digits (1, 2, 3, 4, 5, 6, 7, 8, 9) together in -such a manner that they will make 100. - -105. Also make 100 by using the cipher in addition to the digits. - - -106. How far apart should the knots of a log-line be to indicate -every half-minute, a speed of one mile per hour? - -107. Several persons are bound to pay the expenses of a law process, -which amount to £800, but three of them being insolvent, the rest -have £60 each to pay additional. How many persons were concerned? - - -108. - If five times four are thirty-three, - What will the fourth of twenty be? - - -109. A locomotive with a truck is travelling over a straight level -line at the rate of 60 miles an hour. A man standing at the extreme -rear of the truck casts a small stone into the air in a perpendicular -direction. The stone travels upward at an average rate of 30 feet per -second for 3 seconds; the height of the man’s hand from ground when -the stone leaves is 15 feet. At what distance behind the train will -the stone strike the ground in its descent? - - -A Tombstone in an English Cemetery. - -Many quaint and puzzling epitaphs are often to be seen engraved -on several of the tombstones in some of the old cemeteries at -Home. The adjoining illustration represents a tombstone in the old -burial-ground of London--Kensal Green. It might “liven” up the reader -to discover the scheme of kindred as given in the inscription. - -[Illustration: - - SACRED TO THE MEMORY OF - - TWO GRANDMOTHERS WITH THEIR TWO GRANDDAUGHTERS; - TWO HUSBANDS WITH THEIR TWO WIVES; - TWO FATHERS WITH THEIR TWO DAUGHTERS; - TWO MOTHERS WITH THEIR TWO SONS; - TWO MAIDENS WITH THEIR TWO MOTHERS; - TWO SISTERS WITH THEIR TWO BROTHERS - YET, BUT SIX CORPSES IN ALL LIE BURIED HERE-- - ALL BORN LEGITIMATE FROM ERROR CLEAR.] - -EASILY ANSWERED. - -“Johnny,” said his teacher, “if your father can do a piece of work in -seven days, and your uncle George can do it in nine days, how long -would it take both of them to do it?” - -“They’d never get it done,” said Johnny; “they’d sit down and tell -snake-yarns.” - - -110. A well is to be sunk by 12 men, in groups of 4 each, in 12 days. -The groups work in the ratio of 6, 7, and 8; when half the task is -done rain sets in and prevents them working for 2 days, in which time -one man of the first, 2 of the second, and 3 of the third group go -away, leaving the remainder to finish the job. What extra time did -they work? - - -“TAKE CARE OF THE PENCE, &c.” - -One of the most startling calculations is the following:-- - -A penny at 5 per cent. compound interest from A.D. 1 to 1890 -would amount to £10,000,000,000,000,000,000,000,000,000,000,000,000, -_i.e._, Ten Sextillions of pounds, or more money than could be -contained in One Thousand Millions of Globes each equal to the Earth -in magnitude, and all of solid gold. - - -111. On a flagstaff consisting of an upright pole (6 feet of which is -underground) is a cross-yard 24 feet long; the latter is fixed at a -distance of one-third of the length of the visible part of the pole -from the top; passing from the top of the pole to the ends of the -yard are ropes, forming stays whose falls or ends reach to the ground -on either side of the pole, and it is found that these falls just -reach the base of the pole. The total length of rope in the aforesaid -stays is 40 feet. Supposing that the top diameter of the pole is -one-third of that at the extreme base, and that the whole length of -rope used is 54,177 times the base diameter of the pole, what would -the pole cost at 1 penny per 100 cubic inches? - - -TEACHER--“Your writing is fairly good, but how do you account -for making so many mistakes in your spelling?” - -SCHOLAR--“Please, ma’am, I had chilblains on my hand?” - - -112. Put down 4 marks (| | | |), and then require a person to put -5 more marks and make 10. - - -“KEEP YOUR HAIR ON.” - -113. Supposing there are more persons in the world than anyone -has hairs on his head, there must be at least two persons who have -the same number of hairs on the head to a hair. Explain this. - - -114. Show what is wrong in the following:-- - -8-8 = 2-2, dividing both these equals by 2-2 the result -must be equal; 8-8 divided by 2-2 = 4, and 2-2 divided by -2-2 = 1, therefore, since the quotients of equals divided by -equals must be equal, 4 must be equal to 1. - - -“GLAD TIDINGS.” - -Many will be surprised to hear that there is Scriptural authority -for advertising. Advertising not only has Scriptural authority, -but it is of very respectable antiquity as well. If you will look -in Numbers XXIV., 14, you will find Balaam saying “Come now, and I -will advertise,” and Boaz says in Ruth IV., 4, “And I thought to -advertise.” - - - - -OPTICAL ILLUSIONS. - - -Illusions of the Eye are numberless, and afford a wide field for -experiment. Some people are left-eyed, others right-eyed, and very -few use both eyes equally. It is impossible to tell how far they -really do deceive us unless they have been tested in the proper -manner. For instance, if you ask anyone to what height a bell-topper -would reach if placed on the floor against the wall, nine times out -of ten the height guessed will be half as much again as the real -height of the hat. Everyone seems to _over_-estimate the proper -height. - -[Illustration] - - -Another favourite illusion is to ask a person to mark on the wall a -height from the floor which would represent the length of a horse’s -head: here the majority guess far too little--for a horse’s head is -much longer than most people imagine, ranging from 25 to 34 inches. -In a recent experiment 5 persons out of 6 _under_-estimated the -proper height. - -[Illustration] - - -Here are two triangles. Which is the one whose centre is the better -indicated? (It looks like A, but it is B). - -[Illustration] - -Again: Out of the two straight lines C and D which is the longer? (By -measurement we see they are both the same). - -[Illustration] - -Guess, by eye-measurement only, the longest and shortest of the three -lines marked A A, B B, and C C. When you have done guessing measure, -and see how much you are out. - -[Illustration] - -Which is the tallest gentleman of the three appearing in adjoining -figure?--Many would imagine the last to be the tallest, and the -first the shortest, whereas the reverse is the case--the last is the -shortest, and the first the tallest. - -[Illustration] - -It is surprising how the eye can be deceived, when dealing with areas -or circles. Place on the table a half-crown and a threepenny-piece; -let these be, say, 9 or 10 inches apart, and ask a friend how many -of the latter can be placed on the former--with this proviso: the -threepenny-pieces must not rest on each other, nor must they overlap -the outer rim of the half-crown; they must be fairly within the -circumference of the larger coin. Many will answer 6, 5, or 4, others -who are more cautious 3. Try for yourself and see how many you can -put on, and you are sure to be surprised. - - -ARE THESE LINES PARALLEL? - -The “herring-bone” figure here illustrated is yet another proof that -our eyes are faulty. The horizontal lines appear to slant in the -direction in which the short intersecting lines are falling, and -would give one the idea that they would meet if continued, whereas -really they are parallel. The illusion is more striking if you tilt -the leaf up. - -[Illustration] - - -HOW DID HE DO IT. - -115. Once there was an old tramp who had to go through a tollbar, -and before he could get through he had to pay a penny. He had not a -penny; he did not find a penny, nor borrow a penny, nor steal nor beg -a penny, and yet he paid a penny and went through. - - -116. Find a number which is such that if four times its square be -diminished by 6 times the number itself the remainder shall be 70. - - -117. A man has a certain number of apples; he sells half the number -and one more to one person, half the remainder and one more to a -second person, half the remainder and one more to a third person, -half the remainder and one more to a fourth person, by which time he -had disposed of all that he had. How many had he? - - -TEACHER (impressing one of her _protégés_)--“Be brave and -earnest and you will succeed. Do you remember my telling you of the -great difficulty ‘George Washington’ had to contend with?” - -WILLY RAGGS--“Yes, mum; he couldn’t tell a lie.” - - -118. Two numbers are in the ratio of 2 and 3, and if 9 be added -to each they are in the ratio of 3 to 4. Find the numbers. - - -PAYING A DEBT. - -In an office the boy owed one of the clerks threepence, the clerk -owed the cashier twopence, and the cashier owed the boy twopence. One -day the boy, having a penny, decided to diminish his debt, and gave -the penny to the clerk, who in turn paid half his debt by giving it -to the cashier, the latter gave it back to the boy, saying, “That -makes one penny I owe you now;” the office boy again passed it to the -clerk, who passed it to the cashier, who in turn passed it back to -the boy, and the boy discharged his entire debt by handing it over to -the clerk, thereby squaring all accounts. - - -A TESTIMONIAL. - -“How do you like your new typewriter?” inquired the agent. - -“It’s grand!” was the immediate and enthusiastic response. “I wonder -how I ever got along without it.” - -“Well, would you mind giving me a little testimonial to that effect?” - -“Certainly not; do it gladly.” - -(A few minutes’ pounding). “How’ll this suit you?” - -“afted Using the automatig Back-action a type writ, er for thre -emonthan d Over. I unhesittattingly pronounce it prono nce it to be -al even more than th e Manufacturs claim? for it. During the time -been in our possession e. i. th ree monthzi id has more th an than -paid for it£elf in the saving of time an d labrr? - - John £ Gibbs.” - - -STATE OF THE POLL. - -119. In a constituency in which each elector may vote for 2 -candidates half of the constituency vote for A, but divide their -votes among B, C, D and E in the proportion of 4, 3, 2, 1; half the -remainder vote for B, and divide their votes between C, D, E in -proportion 3, 1, 1; two-thirds of the remainder vote for D and E, and -540 do not vote at all. Find state of poll, and number of electors on -roll. - - -120. Three men, A, B and C, go into an hotel to have a “free and -easy” on their own account, and after sundry glasses of Dewar’s -Whisky got into dispute as to who had the most cash, and neither -being willing to show his hand, the landlord was called upon to -umpire. He found that A’s money and half of B’s added to one-third of -C’s just came to £32, again that one-third of A’s with one-fourth of -B’s and one-fifth of C’s made up £15, again he found that one-fourth -of A’s together with one-fifth of B’s and one-sixth of C’s totalled -£12. How much had each? - -[Illustration] - - -THE BIBLE IN SCHOOLS. - -VISITING CLERGYMAN--“What’s a miracle?” - -BOY--“Dunno.” - -V.C.--“Well, if the sun was to shine in the middle of the -night what would you say it was?” - -BOY--“The moon.” - -V.C.--“But if you were told that it was the sun, what would -you say it was?” - -BOY--“A lie.” - -V.C.--“_I_ don’t tell lies. Suppose _I_ were to tell you it -was the sun, what would you say then?” - -BOY--“That you was drunk.” - - -121. A man travels 60 miles in 3 hours by rail and coach; if he had -gone all the way by rail he would have ended his journey an hour -sooner and saved two-fifths of the time he was on the coach. How far -did he go by coach? - - - WANTED Canvasser, energetic; only “live” - men need apply. Smart & Co. - -A determined-looking young man rushed into Mr. Sharp’s office -the other day, and, addressing him, said abruptly, “See you’re -advertising for a canvasser, sir; I’ve come to fill the place.” - -“Gently, young man!--gently! How do you know that you’ll suit?” asked -Mr. Sharp, somewhat nettled at the young man’s off-hand manner. - -“Certain of it. Best man you could have--energetic, punctual, honest, -sober, A1 references, and----” - -“Wait a minute, I tell you!” shouted Mr. Sharp. “I don’t think you’d -suit me at all.” - -“Oh, yes, I shall,” said the young man, seating himself. “And I don’t -go out of this office till you engage me.” - -“You won’t?” yelled Mr. S. - -“Certainly not,” said the young man, calmly. - -“Why, you impudent young scoundrel! I’ll--I’ll kick you out!” - -“No, you wont. You may kick me, but you won’t kick me _out_.” - -“If you don’t go, I’ll call a policeman,” declared Mr. S., purple -with rage. - -“Will you?” - -The young man rushed to the door, locked it, and put the key in his -pocket. - -Mr. S. gasped and glared, and then roared:-- - -“I tell you I won’t have you! Get out of my office. Will you take -‘no’ for an answer?” - -“No, I won’t take ‘no’ for an answer. Never did in my life, and don’t -intend starting now,” said the young man, very determinedly. - -Mr. Sharp hesitated, then rose to his feet, with admiration beaming -from his eyes. - -“Young man,” he said, “I’ve been looking for an agent like you for -twenty years. At first I thought you were only a bumptious fool; -but now I see you’re literally bursting with business. If any man -can sell my patent vermin-trap (warranted to catch anything from a -flea to a tiger) you’re that man. A hundred a year and 15 per cent. -commission. Is it a bargain?” - -“It is,” said the young man, trying the trap, and smiling approvingly -when it nipped a piece of flesh clean out of his finger. - - -WHY IS IT? - -Take a long narrow strip of paper, and draw a line with pen or pencil -along the whole length of its centre. Turn one of the ends round so -as to give it a twist, and then gum the ends together. Now take a -pair of scissors and cut the circle of paper round along the line, -and you will have two circles. This is a puzzle within a puzzle, -and has never been satisfactorily explained either by scientist or -mathematician. - - -How to Read a Person’s Character. - -Tell a friend to put down in figures the year in which he was born; -to this add 4, then his age at last birthday provided it has not come -in the present year (if it has, then his age last year); multiply -this sum by 1000, and subtract 687,423. (This number is for 1899; -it increases 1000 for each succeeding year.) To the remainder place -corresponding letters of the alphabet. The result will be the popular -name by which your friend is known. - -Example: A person was born in 1860, and is now 38 years of age. - - 1860 - 4 - ---- - 1864 - 38 Age - ---- - 1902 - 1000 - -------- - 1902000 - 687423 - -------------- - 1,2,1,4,5,7,7 - a,b,a,d,e,g,g (“A bad egg.”) - - -122. There are 3 numbers in continued proportion--the middle number -is 60, and the sum of the others is 125. Find the numbers. - - -123. A lends B a certain sum at the same time he insures B’s life for -£737 12s. 6d., paying annual premiums of £20; at the end of three -years and just before the fourth premium is to be paid, B dies, -having never repaid anything. What sum must A have lent B in order -that he may have just enough to recoup himself, together with 5 per -cent. compound interest on the sum lent and on the premiums? - - -124. I met three Dutchmen--Hendrick, Claas, and Cornelius--with their -wives--Gertruig, Catrün, and Anna; in answer to a question they told -me they had been to market to buy pigs, and had spent between them -£224 11s; Hendrick bought 23 pigs more than Catrün, and Class bought -11 more than Gertruig, each man laid out 3 guineas more than his -wife. Now find out each couple--man and wife. - - -CURIOUS BOOK-KEEPING. - -An old tradesman used to keep his accounts in a singular manner. He -hung up two boots--one on each side of the chimney; into one of these -he put all the money he received, and into the other all the receipts -and vouchers for the money he paid. At the end of the year, or -whenever he wanted to make up his accounts, he emptied the boots, and -by counting their several and respective contents he was enabled to -make a balance, perhaps with as much regularity and as little trouble -as any book-keeper in the country. - - -QUICKER THAN THOUGHT. - -A little boy, hearing someone remark that nothing was quicker than -thought, said: “I know something that is quicker than thought.” “What -is it, Johnny?” asked his pa. “Whistling,” said Johnny. “When I was -in school yesterday I whistled before I thought, and got caned for -it, too.” - - -125. The number of men in both fronts of two columns of troops A and -B, when each consisted of as many ranks as it had men in front, was -84; but when the columns changed ground, and A was drawn up with the -front B had, and B with the front A had; the number of ranks in both -columns was 91. Required: the number of men in each column. - - -RUNNING THROUGH HIS FORTUNE. - -126. A man inheriting money spends on the first day 19s., twice that -amount on the next, and 19s. additional every day till he exhausts -his fortune by spending on the last day £190 by way of having a real -good time of it and treating his friends to a good “blow out.” What -amount of money had he left to him at the start? - - -127. A shopkeeper makes on a certain article the first day a profit -of 3d., the second day 4·2d., and so on, profit increasing each day -by 1·2d. He had a profit of 14s. 3d. on the whole. How many days was -he selling the article? - - -“AWFUL SACRIFICE.” - -One of those generous, disinterested, self-sacrificing tradesmen, -having stuck upon every other pane of glass in his window, -“Selling-off,” “No reasonable offer refused,” “Must close on -Saturday,” offered himself as bail, or security, in some case -which was brought before a magistrate, when the following dialogue -ensued:--The magistrate asking him if he was worth £200, “Yes,” he -replied. “But you are about to remove, are you not?” “No.” “Why, you -write up, ‘Selling-off.’” “Yes, every shopkeeper is selling off.” -“You say, ‘No reasonable offer will be refused.’” “Well, I should be -very unreasonable if I did refuse such offers.” “But you say, ‘Must -close on Saturday.’” “To be sure; you would not have me open on -Sunday, would you?” - - -128. A man dying left his property of £10,000 to his four children, -aged respectively 6, 8, 10, and 12 years, on the understanding that -each on attaining his majority shall receive the same amount of -money, comp. interest at the rate of 4½ per cent. being allowed. -What is the amount of the £10,000 payable to each? - - -A WASTE OF TIME. - -A little boy spent his first day at school. “What did you learn?” was -his aunt’s question. “Didn’t learn nothing.” “Well, what did you do?” -“Didn’t do nothing. There was a woman wanting to know how to spell -‘cat,’ and I told her.” - - -An English School-boy’s Essay on Australia. - -“Part of Austrailya is vague. It ust to be used by the English to -keep men on that was not bad enough to be killed. Some farms would -raise as much as five hundred thousand. The English long ago ust to -send their prisoners there when they did anything not worth hanging. - -“Austrailya is a vast Country, and the biggest Island on the surface -of the Earth. It has all its bad men and they have found a great many -Gold and Diamonds there, and Sidney is one of the Chief Countries in -it which is in new south Wales. - -“It used to be used for purposes of Exploration, but it has no -interior, and you can’t explore it. Sometimes it is called Antipides, -because everything is upside down there. The chief products are Wool -and Gold and other Exports and the Austrailyan eleven come from -there. The Climate is hot in the Summer and not so in the Winter, -which causes drowts and sweeps all the sheep away and the banks break. - -“It was discovered by Captain Cook who captured it from the Dutch. -There are no wild Animals there except the Kangaroo, they fly -through the air with great skill and then they return again right to -your feet. The natives are coloured Black and they call themselves -Aboriginels, they subsist on bark and other food they do no work and -chop wood for a miserable living and can smell the ground like a -dog. When we go there they call us new Chums. They have no form of -Worship, and pray for rain, but a belief in Federashun because they -want to be joined together. - -“Their only amusement is Co-robbery. It is celebrated for -Bushrangers and the Melbourne Cup which sticks people up and takes -from them all they have got. - -“Austrailya has a lot of aliasses, one is new Holland and afterwards -it was called Pollynesia, and Van Demon and Oceana but sir Henry -Parks called it Austrailya on his Death-bed. You can go to it in a -ship but it is joined to Great Britain by a cable.” - - -129. I ran to a certain railway station to meet the train which was -due at 3.15 p.m. When I arrived on the platform the hands of the -clock made equal angles with 3 o’clock. How long had I to wait? - -[Illustration] - - -130. The wall of China is 1500 miles long, 20 feet high, 15 feet wide -at the top and 25 at the bottom. The largest of the pyramids is said -to have been 741 feet at the base, 481 feet vertical when finished. -How many such pyramids could be built out of the wall of China? - - -GRAMMAR. - -SCHOOLMASTER--“Now, boys, the word ‘with’ is a very bad word -to end a sentence with.” - - -131. There is an arch of quadrantal form; the rise of the crown -is 17 feet. What is the span? - - -132. - Two pairs of fives I bid you take, - And four times four and forty make. - - -133. A lady bought a quantity of flannel, which she distributed among -some poor women; the first received 2 yards, the second 4 yards, and -so on; the lot cost her £5 14s. 2½d. How many women were there, and -what did the lady pay per yard? - - -134. A and B marry, their respective ages being in proportion to 3 -and 4. Now after they have been married 14 years their ages are as 5 -to 6, and the age of A is 5 times that of her youngest child, who was -born when the parents’ ages were as 4 to 5. Required: the ages of A -and B when they were married, and the age of the youngest child now -that they have been married 14 years. - - -AN APPALLING “SUM.” - -At a school, a short time back, the pupils were given, as a home -lesson, the task of subtracting from 880,788,889 the number 629 so -often till nothing remained. - -The boys worked on for hours without any perceptible diminution of -the figures, and at length gave up the task in despair. Some of the -parents then tried their hands, with no better success. For, in order -to work out the sum, the number 629 would have to be subtracted -1,400,300 times, leaving 189 as a remainder. - -Working 12 hours a day, at the rate of 3 subtractions per minute, it -would take over 1 year and 9 months to complete the sum which had -been set the poor lads for their home lesson. - - -A MILITARY LUNCHEON. - -135. A certain number of Volunteers--namely, Commissioned Officers, -Non-commissioned Officers, and Privates had a dinner bill to pay; -there were, it seemed, half as many more Non-Com. Officers as Com., -one-third as many more Privates as Non-Com. Officers, and they agreed -that each Commissioned Officer should pay one-third as much again -as each Non-Com., and each Non-Com. one-fifth as much again as each -Private; but 1 Commissioned and 2 Non-Com. Officers slipped away -without paying their portion (5s.), each of the others had to pay in -consequence 4d. more. What was the amount of the bill, and the number -of each present? - - -Twice the half of 1½? Ask your friends--it bothers them. - - -The Problem Easily Solved. - -“Do you see that row of poplars on the other bank standing apparently -at equal distances apart?” asked a grave-faced man of a group of -people standing by a river. - -The group nodded assent. - -“Well, there’s quite a story connected with those trees,” he -continued. “Some years ago there lived in a house overlooking the -river a very wealthy banker, whose only daughter was beloved by a -young surveyor. The old man was inclined to question the professional -skill of the young rod and level, and to put him to the test directed -him to set out on the river shore a row of trees, no two of which -should be any further apart than any other two. The trial proved -the lover’s inefficiency, and forthwith he was forbidden the house, -and in despair drowned himself in the river. Perhaps some of you -gentlemen with keen eyes can tell me which two trees are furthest -apart?” - -The group took a critical view of the situation, and each member -selected a different pair of trees. Finally, after much discussion, -an appeal was made to the solemn-faced stranger to solve the problem. - -“The first and the last,” said he, calmly, resuming his cigar and -walking away with the air of a sage. - - -136. - Twice five of us are eight of us, and two of us are three, - And three of us are five of us--now how can all this be? - If that does not puzzle you I’ll tell you one thing more: - Eight of us are five of us and five of us are four. - - -“EXPRESSIONAL” MEASURES. - -The table of measures says that 3 barleycorns make 1 inch--and so -they do. When the standards of measures were first established 3 -barleycorns, well-dried, were taken out and laid end to end, and -measured an inch. - -The “hairbreadth” now used indefinitely for infinitesimal space, was -a regular measure, 16 hairs laid side by side equalling 1 barleycorn. - -The expression “in a trice,” as everyone knows, means a very short -space of time. The hour is divided into 60 minutes, the minute into -60 seconds, and the second into 60 “trices.” - - -A CHALLENGE. - -137. A lady belonging to the W.C.T.U. was endeavouring to persuade a -gentleman friend of hers to give up the drink; he replied, “I will -sign the pledge if you tell me how many glasses of beer did I drink -to-day if the difference between their number and the number of times -the square root of their number is contained in 2 be equal to 3.” - - -MEMORY SYSTEM. - -TEACHER--“In what year was the battle of Waterloo fought?” - -PUPIL--“I don’t know.” - -TEACHER--“It’s simple enough if you only would learn how to -cultivate artificial memory. Remember the twelve apostles. Add half -their number to them. That’s eighteen. Multiply by a hundred. That’s -eighteen hundred. Take the twelve apostles again. Add a quarter of -their number to them. That’s fifteen. Add to what you’ve got. That’s -1815. That’s the date. Quite simple, you see, to remember dates if -you will only adopt my system.” - - -A GLOBE TROTTER. - -138. Everyone knows that in a race on a circular track the competitor -who has the “inside” running has the least ground to cover, hence the -great desire of cyclists, jockeys, &c., to “hug the fence.” - -Now a gentleman, six feet high, starts walking round the Earth on -the equator; his feet, therefore, have the inside running. Find out -how much further his head travels than his feet in performing this -wonderful journey? taking the circumference of the globe at the -equator to be 25,000 miles. - -[Illustration] - - -PRECOCIOUS JUVENILE--“Mamma, it isn’t good grammar to say -‘after I,’ is it?” - -HIS MOTHER--“No, Georgie.” - -PRECOCIOUS JUVENILE--“Well, the letter J comes after I. -Which is wrong--the grammar or the alphabet?” - - -139. There is an island in the form of a semi-circle; two persons -start from a point in the diameter; one walks along the diameter, and -the other at right angles to it; the former reaches the extremity of -the diameter after walking 4 miles, and the latter the boundary of -the island after walking 8 miles. Find the area of the island. - - -140. There is a certain number consisting of three figures which is -equal to 36 times the sum of its digits, and 7 times the left-hand -digit plus 9, equal to 5 times the sum of the remaining digits, and 8 -times the second digit minus 9 is equal to the sum of the first and -third. What is the number? - - -141. A bottle and cork costs 2½d.; the bottle costs 2d. more than -the cork. What is the price of each? - - -A Cure for Big Words. - -Here is a good story of how a father cured his son of verbal -grandiloquence. The boy wrote from college, using such large -words that the father replied with the following letter:--“In -promulgating your esoteric cogitations, or articulating superficial -sentimentalities, and philosophical or pscyhological observations, -beware of platitudinous ponderosity. Let your conversation possess -a clarified conciseness, compacted comprehensibleness, coalescent -consistency, and a concatenated cogency. Eschew all conglomerations -of flatulent garrulity, jejune babblement, and asinine affectations. -Let your extemporaneous descantings and unpremeditated expatiations -have intelligibility, without rhodomontade or thrasonical bombast. -Sedulously avoid all polysyllabical profundity, pompous prolixity, -and ventriloquial vapidity. Shun double entendre and prurient -jocosity, whether obscure or apparent. In other words, _speak -truthfully, naturally, clearly, purely, but do not use big words_.” - - -142. With a pair each of four different weights, 1 lb. up to 170 lbs. -can be weighed. What are the weights? - - -143. A man going “on the spree” spends on the first day 10s. 5d., the -second 18s., the third £1 8s. 7d., the fourth £2 2s. 8d., and so on -at that rate of increase until he has spent all he had--£183 6s. 8d. -How many days was he on the spree? - - -144. Divide one shilling into two parts, so that one will be 2½d. -more than the other. - - -COMPLIMENTARY, VERY! - -EDITOR--“Did you see the notice I gave you yesterday?” - -SHOPKEEPER--“Yes, and I don’t want another. The man who says -I’ve got plenty of grit, and that the milk I sell is of the first -water, and that my butter is the strongest in the market, may mean -well, but he is not the man whose encomiums I value.” - - -145. A vintner draws a certain quantity of wine out of a full vessel -that holds 256 gallons, and then filling the same vessel with water -draws off the same quantity of liquor as before, and so on for four -draughts, when only 81 gallons of pure wine is left. How much wine -did he draw each time? - - -146. A man has 4 horses, for which he gave £80; the first horse cost -as much as the second and half of the third, the second cost as much -as the fourth minus the cost of the third, the third cost one-third -of the first, and the fourth cost as much as the second and third -together. What was the price of each horse? - - -The Divided Pound. - -147. A father wishes to divide £1 between his four sons, giving -one-third to one, one-fourth to another, one-fifth to another, and -one-sixth to another; in doing so he finds he has only disbursed -19s.; the balance, 1s., is then divided in the same proportion. What -amount does each receive in full in the proportion named? - - -RAILWAY-SHUNTING PUZZLE. - -148. A locomotive is on the main line of railway; the trucks marked -1 and 2 are on sidings which meet at the points, where there is room -for one truck only and not for the locomotive. It is desired to -reverse the position of the trucks--that is, put 1 where 2 is, and -2 where 1 is, and yet leave the locomotive free on the main line. -This must be done by means of the locomotive only, either pulling -or pushing the trucks--it may be between them, thus pulling one and -pushing the other--but no truck must move without the locomotive. - -[Illustration] - -In working this puzzle out, it would be best to draw the diagram -on an enlarged scale, and have articles to represent the trucks and -locomotive. - - -149. In a public square there is a fountain containing a quantity -of water; around it stand a group of people with pitchers and -buckets. They draw water at the following rate: The first draws -100 quarts and one-thirteenth of the remainder, the second 200 quarts -and one-thirteenth of the remainder, the third 300 quarts and -one-thirteenth, and so on, until the fountain was emptied. How many -quarts were there in the fountain? - - -ENGLISH FROM A GERMAN MASTER. - -PROF. GOLDBURGMANN--“Herr Kannstnicht, you will the -declensions give in the sentence, “I have a gold mine.” - -HERR KANNSTNICHT--“I have a gold mine; thou hast a gold -thine; he has a gold his; we, you, they have a gold ours, yours, or -theirs, as the case may be.” - -PROF. GOLDBURGMANN--“You right are; up head proceed. Should -I what a time pleasant have if all Herr Kannstnicht like were!” - - -SPENDING THEIR “ALL.” - -150. Three men going “on the spree” decide to spend all their money. -The first, A, “shouts” for the company and then gives his balance to -B, who also in turn pays for 3 drinks and gives his balance to C, who -can then just manage to pay for drinks once more at 6d. each. How -much money had each? - - -151. There is a regiment of 7300 soldiers, which is to be divided -into 4 companies--half of the first company, two-thirds of the -second, three-quarters of the third, and four-fifths of the -fourth--to be composed of the same number of men. How many soldiers -are there in each company? - - -A GRAVE MISTAKE. - -A Scotch tradesman, who had amassed, as he believed, £4000, was -surprised at his old clerk’s showing by a balance-sheet his fortune -to be £6000. “It canna be--count again,” said the old man. The clerk -did count again, and again declared the balance to be £6000. Time -after time he cast up the columns--it was still a 6, and not a 4, -that rewarded his labours. So the old merchant, on the strength of -his good fortune, modernised his house, and put money in the purse -of the carpenter, the painter, and the upholsterer. Still, however, -he had a lurking doubt of the existence of the extra £2000; so one -winter’s night he sat down to give the columns “one count more.” At -the close of his task he jumped up as though he had been galvanised, -and rushed out in a shower of rain to the house of the clerk, who, -capped and drowsy, put out his head from an attic window at the sound -of the knocker, mumbling, “Who’s there, and what d’ye want?” “It’s -me, ye scoundrel!” exclaimed his employer. “Ye’ve added up the year -of our Lord amang the poons!” - - -PROBLEM FOR PRINTERS. - -152. A book is printed in such a manner that each page contains a -certain number of lines, and each line a certain number of letters. -If each page contains 3 lines more, and each line 4 letters more, the -number of letters in each page will be 224 more than before; but if -each page contains 2 lines less, and each line 3 letters less, the -number of letters in each page would be 145 less than before. Find -the number of lines in each page, and the number of letters in each -line. - - -THE INCOME TAX. - -153. The charge on a major income is the same in amount as that on a -minor one, which is 2½ per cent. of their mutual difference, but -the rate imposed on the overplus of a major income is 4 per cent., so -that on a composite income of the major and minor the charge would be -£3 8s. Required the major and minor incomes. - - -“Your Money or Your Life!” - -154. Two gentlemen, A and B, with £100 and £48 respectively, having -to perform a long journey through a lonely part of the country, agree -to travel together for purposes of safety; they are, however, taken -unawares by a gang of bushrangers who, calling upon them to “bail -up,” ease them of some of their cash. The leader of the gang was -satisfied with taking twice as much from A as from B, and left to A -three times as much as to B. How much was taken from each? - -[Illustration] - - -GEOMETRICAL MUSIC. - - · A point, my boys, is that which has no length, breadth, - or dimension. - -- A line has length, and yet is but a point drawn in extension. - All lines have names expressing some distinguishing particular. - As: horizontal, parallel, oblique, and perpendicular. - _Chorus of Pupils._ Oh! dear! oh! - A pretty science mathematics is to know. - - The lines called parallel are those which, drawn in one direction, - Continued to infinity, will never make bisection. - The thing perhaps sounds odd, but if you entertain a doubt, boys, - I’ll draw the lines, ====== now take your slates, and work the - problem out, boys. - - _Chorus of Pupils._ Oh! dear! no! - We readily believe it, Sir! since _you_ say so! - - -155. In this figure rub out eight lines, and leave two squares. No side -nor angle of any square must be left, otherwise that will be counted as -a square. - -[Illustration] - - -156. A and B travelled by the same road, and at the same rate from -Tamworth to Sydney. A overtook a flock of sheep, which travelled at -the rate of three miles in two hours, and two hours after he met a -mail coach, which travelled at the rate of nine miles in four hours. -B overtook the flock 45 miles from Sydney, and met the coach 40 -minutes before he came to the 31-mile post from the Metropolis. Where -was B when A reached Sydney? - - -ENGLISH HISTORY. - -A school examination paper contained the question:--“Write down all -you know about Henry VIII,” and one of the small boys answered as -follows:-- - -“King Henry 8 was the greatest widower that ever lived. He was born -at Anne Domini in the year 1066. He had 510 wives besides children. -The first was beheaded and afterwards executed, and the second was -revoked. She never smiled again. But she said the word ‘Calais’ would -be found on her heart after death. The greatest man in this reign -was Lord Sir Garret Wolsey--named the Boy Bachelor. He was born at -the age of fifteen unmarried. Henry 8 was succeeded on the throne by -his great-grandmother, the beautiful Mary, Queen of Scots, sometimes -called Lady of the Lake or the Lay of the Last Minstrel.” - - -157. Two boys, A and B, run round a ring in opposite directions till -they meet at the starting point, their last meeting place before this -having been 990 yards from it. If A’s rate to B’s be as 5 to 3, find -the distance they have travelled. - - -THE VALUE OF HOME LESSONS. - -Two teachers of languages were discussing matters and things relative -to their profession. - -“Do your pupils pay up regularly on the first of each month?” asked -one of them. - -“No, they do not,” was the reply; “I often have to wait weeks and -weeks before I get my pay, and sometimes I don’t get it at all. You -can’t well dun the parents for the money.” - -“Why don’t you do as I do? I always get my money regularly.” - -“How do you manage it?” - -“It is very simple. For instance, I am teaching a boy French, and -on the first day of the month his folks don’t send the amount due -for the previous month. In that case I give the boy the following -exercise to translate and write out at home:--‘I have no money. The -month is up. Hast thou any money? Have not thy parents any money? I -need money very much. Why hast thou brought no money this morning? -Did thy father not give thee any money? Has he no money in the -pocket-book of his uncle’s great aunt?’ This fetches them. Next -morning that boy brings the money.” - - -158. There is a number half of which divided by 6, one-third of it -divided by 4, and one-fourth of it divided by 3, each quotient will -be 9. What is the number? - - -QUIBBLE. - -159. - Two-thirds of six is nine, one-half of twelve is seven, - The half of five is four, and six is half of eleven. - - -SOMETHING EASY. - -160. Find a sum of £ s. d. (no farthings) in which the figures, in -their order, represent the amount reduced to farthings. - - -161. Three persons won a “consultation” worth £1,320. If J were to -take £6, M ought to take £4, and B £2. What is each person’s share? - - -“ON THE JOB.” - -162. Six masons, four bricklayers and five labourers were working -together at a building, but being obliged to leave off one day by the -rain, they went to a public-house and drank to the value of 45s., -which was paid by each party in the following manner: Four-fifths -of what the bricklayers paid was equal to three-fifths of what the -masons paid, and the labourers paid two-sevenths of what the masons -and bricklayers paid. What did each party of men pay? - -[Illustration] - - -163. In a certain speculation I gained £4 19s. 11¾d. for each -pound I expended, and by a curious coincidence I found that £4 19s. -11¾d. was the exact amount I had ventured. Required the amount of -capital and profit together. - - -HIS MAJORITY. - -164. “I am not a man, I suppose, till I am 21. How long have I to -wait yet, if the cube root of my age eight years hence, added to the -cube root of my age eleven years ago would make 5?” - - -DRAUGHT-BOARD PUZZLE. - -165. Place eight men on a draught-board in such a way that no two -will be in a line either crossways or diagonally. Of course the two -colours on the board must be used. - - -166. A gentleman, dying, left his property thus: To his wife, -three-fifths of his son’s and youngest daughter’s shares; to his -son, four-fifths of his wife’s and eldest daughter’s shares; to his -eldest daughter, two-sevenths of his wife’s and son’s shares, and to -his youngest daughter one-sixth of his son’s and eldest daughter’s -shares. The wife’s share was £4,650. What did the gentleman leave, -and what did each receive? - - -SAMSON OUTDONE. - -A man boasted that he carried off an entire timber yard in his left -hand. It turned out that the timber-yard was a three-foot rule. - - -Domino Puzzle. - -[Illustration] - -167. Arrange the 28 dominoes in such a manner as to have two squares -of each number; there are eight half-squares of each number in the -complete set--eight sixes, eight fives, &c.--so that four of the -one number comprise a square. The whole, when finished, will form a -figure like a square, resembling a wide letter =I=. - -[Illustration] - - -168. A sum of money is divided among a number of persons; the second -gets 8d. more than the first, the third gets 1s. 4d. more than the -second, the fourth 2s. more than the third, and so on. If the first -gets 6d. and the last £5 2s. 6d., how many persons were there? - - -IT COULDN’T BE EXPECTED. - -Teacher: “Johnny, where is the North Pole?” - -Johnny: “I don’t know.” - -Teacher: “Don’t know where the North Pole is?” - -Johnny: “When Franklin, Nansen and Captain Andrée hunted for it and -couldn’t find it, how am I to know where it is?” - - -169. For a loan of 2,500,000, 4½ per cent. per annum is paid by -a mining company whose capital is £4,900,000. The working expenses -constitute 52 per cent. of the gross receipts, which amount in the -year to £965,000, and the directors set apart £44,450 as a reserve -fund. What yearly dividend do the shareholders receive? - - -170. If a monkey climbs a greasy pole 10 ft. high, ascending 1 ft. with -each movement of his arms, and slipping back 6 in. after each advance; -how many movements would he have to make, to touch the top, and what -height would he have climbed in all? - - -171. Find two numbers whose G.C.M. is 179, L.C.M. 56385, and -difference 10382. - - -172. What is the difference between twenty four-quart bottles, and -four and twenty quart bottles? - - -THE G.C.M. - -The Greatest Common Measure--A “long pint.” - -173. There are two casks, one of which holds thirty gallons more than -the other. The larger is filled with wine, the smaller with water. -Ten gallons are taken out of each: that from the first is poured into -the second; the operation is repeated, and it is now found that the -larger cask contains 13 gallons of water. Find the contents of each -cask. - - -174. - In the midst of a paddock well stored with grass, - I engaged just an acre to tether my ass; - What length must that cord be, in grazing all round - That he may graze over just one acre of ground? - -175. If three first-class cost as much as five second-class tickets -for a journey of 100 miles, the total cost of the eight tickets -being £3 2s. 6d., find the charge per mile for each first-class and -second-class ticket. - - -HUMILITY. - -In a certain street are three tailors. The first to set up shop hung -out this sign--“Here is the best tailor in the town.” The next put -up--“Here is the best tailor in the world.” The third simply had -this--“Here is the best tailor in this street.” - - -“On the Wallaby.” - -176. Four sundowners called at a station and asked for rations. -“Well,” said the manager, “I have a job that will take 200 hours to -complete; if you want to do it, you can divide the work and the money -among yourselves as you see fit.” The sundowners agreed to do the -work on these conditions. “Now, mates,” said the laziest of them, -“it’s no good all of us doing the same amount of work. Let’s toss -up to see who shall work the most hours a day, and who the fewest. -Then let each man work as many days as he does hours a day.” This -was agreed to; but the proposer took good care that chance should -designate him to do the least number of hours of work. How were the -200 hours put in so that each man should work as many hours as days, -and yet no two men work the same number of hours? - - -177. On multiplying a certain number by 517 a result is obtained -greater by 7,303,535 than if the same number had been multiplied -by 312. How much greater still would be the result if 811 were the -multiplier instead of 312? - - -A “CATCH.” - -178. Six ears of corn are in a hollow stump. How long will it take a -squirrel to carry them all out if he takes but three ears a day? - - -NUMBER 7. - -The number 7 has always been considered the most sacred of all our -figures. Its prominence in the Scriptures is very remarkable, from -Genesis--where we read that the seventh day was consecrated as a day -of rest and repose--to Revelations--where we find the seven churches -of Asia; seven golden candlesticks; the book with seven seals; the -seven angels with seven trumpets; seven kings; seven thunders; seven -plagues, &c., &c., its frequent occurrence is most striking. - -The Ancients paid great respect to the seven mouths of the Nile. -The seven rivers of Vedic India; seven wonders of the world; seven -precious stones; seven notes of music; seven colours of the rainbow, -&c., &c. The “Lampads seven that watch the Throne of Heaven” led -the Chaldeans to esteem the unit 7 as the holiest of all numbers, -thereupon they established the week of seven days, and built their -temples in seven stages. The temples and palaces of Burma and China -are seven-roofed. - -In modern times this number has kept up its reputation. Shakespeare -paid special regard to it; the “seven ages” and every multiple of it -is supposed to be a critical or important period in one’s life. - -A modern philosopher as follows apportions-- - -MAN’S FULL EXTREME. - - 7 years in childhood, sport and play, (7) - 7 years in school from day to day, (14) - 7 years at trade or college life, (21) - 7 years to find a place and wife, (28) - 7 years to pleasure’s follies given, (35) - 7 years to business hardly driven, (42) - 7 years for some wild-goose chase, (49) - 7 years for wealth, a bootless race, (56) - 7 years of hoarding for your heir, (63) - 7 years in weakness spent and care, (70) - And then you die and go--you know not where. - -Very many superstitious and curious ideas have been and still are -connected with all our figures. For those interested in this subject -see page 146--“How To Become Quick At Figures” (Student’s Edition). - - -“What’s the difference,” asked a teacher in arithmetic, “between one -yard and two yards?” “A fence,” said Tommy Yates. Then Tommy sat on -the ruler 14 times. - - -179. What relation is a woman to me who is my mother’s only child’s -wife’s daughter? - - -THE ADVANTAGES OF SKILFUL BOOK-KEEPING. - -If a merchant wishes to get pretty deeply in debt, and then get rid -of his liabilities by bankruptcy--if, in fact, he proposes to himself -to go systematically into the swindling business, and engage in -wholesale pecuniary transactions without a shilling of his own, the -first thing he should take care to learn would be the whole art of -book-keeping. - -From what may occasionally be seen of the reports of the proceedings -in bankruptcy, it is found that _well kept books_ are regarded as -quite a test of honesty, and though assets may have disappeared or -never have existed, though large liabilities may have been incurred -without any prospect of payment, the bankrupt will be complimented -on the straight look of his dealings, if he has shown himself a good -book-keeper. - -To common apprehension it would seem that well kept books would only -help to show a reckless trader the ruinous result of his proceedings, -and that while the man _without_ books might flatter himself that -all would come out right at last, the man with exact accounts would -only get into hot water with his eyes open. If a man may trade on -the capital of others without any of his own, and get excused on the -ground that he has kept his books correctly, it is difficult to see -why a thief who steals purses, &c., may not plead in mitigation of -punishment that he has carefully booked the whole of his transactions. - -It would be interesting to know the effect of producing a ledger -on a trial for felony, as well as curious to observe whether a -burglar would be leniently dealt with on the ground that his -house-breaking accounts gave proof of his experience in the science -of “double-entry.” - -Therefore it would be well for those interested to procure copies of -“RE ACCOUNTS” and “ADVANCED THOUGHT ON ACCOUNTS.” - - -THE FIRM HE REPRESENTED. - -A commercial traveller handed a merchant upon whom he had called a -portrait of his sweetheart in mistake for his business card, saying -that he represented that establishment. The merchant examined it -carefully, remarked that it was a fine establishment, and returned it -to the astonished and blushing traveller with the hope that he would -soon be admitted into partnership. - - -180. A man and a boy being paid for certain days’ work, the man -received 27s., and the boy, who had been absent 3 days out of the -time, received 12s. Had the man, instead of the boy, been absent the -3 days they would both have claimed an equal sum. Find out the wages -of each per day. - - -181. The extremes of an arithmetical series are 21 and 497, and the -number of terms is 41. What is the common difference? - -182. A wine which contains 7½ per cent. of spirit is frozen, and -the ice which contains no spirit being removed the proportion of -spirit in the wine is increased by 8¾ per cent. How much water in -the shape of ice was removed from 504 gallons of the mixture? - - -THE SHARP SELECTOR. - -183. A selector rented a farm, and agreed to give his landlord -two-fifths of the produce, but prior to the time of dividing the corn -the selector used 45 bushels. When the general division was made it -was proposed to give to the landlord 18 bushels from the heap in lieu -of the share of the 45 bushels which the tenant had used, and then to -begin and divide the remainder as though none had been used. Would -this method have been correct? - - -A GOOD “AD.” - -A member of a certain firm appeared in a law court with a complaint -that his partner would sell goods at less than cost price, and he -desired to have him restrained. The defendant utterly denied the -charge, and the case was adjourned for a fortnight. As the plaintiff -went out of court he exclaimed in a tragic tone: “Then the sacrifice -must still go on!” and “I’ll be ruined!” The story was noised -abroad, and the result was that the shop was besieged by customers -every day. There the case ended, for at the end of the fortnight -the plaintiff failed to appear in court, having accomplished his -purpose--advertisement. - - -184. I give 3 sovereigns for 2 dozen wine at different rates per -dozen, and by selling the cheaper kind at a profit of 15 per cent. -and the dearer at a loss of 8 per cent. I obtain a uniform price for -both. What did each dozen cost me? - - -185. I have in my garden a shrub that grows 12 inches every day, but -during the night it withers off to half the height that it was at the -end of the previous day. How much short of 2 feet will it be at the -end of a year? - - -TIT-FOR-TAT. - -186. A farmer puts a 3 lb. stone in a keg of butter worth 11d. a -pound. The merchant cheats him out of 1 lb. on the weight, and then -does him out of 1s. 11d. on calico, tobacco, and a shovel. Who is -ahead, and how much? - - -187. Trains leave London and Edinburgh (400 miles apart) at the same -time and meet after 5 hours; the train which leaves London travels 8 -miles an hour faster than that which leaves Edinburgh. At what rate -did the former travel, and at what speed must the latter travel after -they have met, in order that they both may reach their destinations -at the same time? - - -“GOOD ENOUGH!” - -“Will you give me a glass of beer, please?” asked a rather -seedy-looking fellow with an old but well-brushed coat and almost too -shiny a hat. It was produced by the barmaid, frothing over the edge -of the tumbler. - -“Thank you,” said the recipient, as he placed it to his lips. Having -finished it in a swallow, he smacked his lips and said, “That is very -good beer--_very_! Whose is it?” - -“Why, that Perkins’s----” - -“Ah! Perkins’s, is it! Well, give us another glass.” - -It was done; and holding it up to the light and looking through it, -the connoisseur said:-- - -“’Pon my word, it is grand beer--clear as Madeira! What a fine color! -I must have some more of that; give me another glass.” - -The glass was filled again, but before putting it to his lips the -imbiber said:-- - -“_Whose_ beer did you say this was?” - -“Perkins’s,” emphatically replied the barmaid. - -The contents of the glass was exhausted, as also the vocabulary of -praise, and it only remained for the appreciative gentleman to say, -as he wiped his mouth and went towards the door:-- - -“Perkins’s beer, is it! I know Perkins very well; I shall see -him soon, and will settle with him for three long glasses of his -incomparable brew. Good morning.” - - -A Conspiracy. - -188. Three gentlemen are going over a ferry with their three -servants, who conspire to rob them if they can get one gentleman to -two of them, or two to three, on either side of the ferry. They have -a boat that will only carry two at once, and either a gentleman or a -servant must bring back the boat each time a cargo of them goes over. -How can the gentlemen get over with all their servants so as to avoid -an attack? - - -189. Find two numbers whose product is equal to the difference of -their squares, and the sum of their squares equal to the difference -of their cubes? - - -190. Divide 1400 into such parts as shall have the same ratio as the -cubes of the first four natural numbers. - - -This was the tempting notice lately exhibited in the window of a -dealer in cheap shirts: “They won’t last long at this price!” - - -POSTING THE LEDGER. - -The well known author of several works on account-keeping, Mr. -Yaldwyn, tells a rather good thing which actually occurred in New -Zealand some time back. Mr. Yaldwyn was at the time engaged examining -the books in one of the offices in a country town, and enquired -from one of the clerks standing near if the ledger were posted. -The person appealed to answered that “he didn’t know,” whereupon -Mr. Y. said that he required it done, and with as little delay as -possible. A few minutes later the same individual came rushing in and -informed him that the ledger was “posted.” Such a piece of “lightning -book-keeping” so surprised Mr. Y. that he further questioned the man, -who replied “You said you wanted the ledger posted, and, begorra, I -posted it.” It then dawned upon Mr. Yaldwyn that the clerk, who was -an Irishman, had actually _posted_ the book in the post office! - - -THEY MANAGED IT. - -[Illustration] - -191. Billy and Tommy, two aboriginals, killed a kangaroo in the bush, -and began quarrelling over the weight of the animal. They had no -proper means of weighing it, but, knowing their own weights, Billy -130 lbs. and Tommy 190 lbs., they placed a log of wood across a stump -so that it balanced with one on each end. They then exchanged places, -and, the lighter man taking the kangaroo on his knees, the log again -balanced. What was the weight of the kangaroo? - - -192. A son asked his father how old he was, and received the -following answer: “Your age is now one quarter of mine, but five -years ago it was only one-fifth.” How old is the father? - - -193. Place three sixes together so as to make seven. - - -THE PASSING TRAINS PUZZLE. - -194. If through passenger trains running to and from New York and San -Francisco daily start at the same hour from each place (difference -of longitude not being considered) and take the same time--seven -days--for the trip, how many such trains coming in an opposite -direction will a train leaving New York meet before it arrives at San -Francisco? - - -THE SCHOOL-TEACHER “CAUGHT.” - -Two of our Public Schools were engaged playing a football match one -afternoon. The head master of one of them had generously given the -boys a half-holiday; but the gentleman who held the same capacity in -the other school, not being an ardent admirer of Australia’s national -game, refused to do so. When school assembled in the afternoon, a -boy volunteered to ask the master for the desired holiday. When the -question was put, he firmly answered, “No, no!” whereupon the bright -youth called out: “Hurrah! we have our holiday; two negatives make an -affirmative.” The teacher was so pleased at the boy’s sharpness that -he dismissed the school right away. - - -195. A man arrives at the railway station nearest to his home 1½ -hours before the time at which he had ordered his carriage to meet -him. He sets out at once to walk at the rate of four miles an hour, -and, meeting his carriage when it had travelled eight miles, reaches -home exactly one hour earlier than he had originally expected. How -far was his house from the station, and at what rate was his carriage -driven? - - -“OFF THE TRACK.” - -196. A man starts to walk from a town, A, to a town B, a distance by -road of 16 miles, at the rate of 4 miles an hour. There is a point -C on the road, at which the road to B leads away to the right, and -another road at right-angles to this latter goes to the left, “to no -place in particular.” The unwary traveller gets on to this left hand -road, and is walking for 2¼ hours since he left A, before he finds -out his mistake, and he resolves not to go back to the junction, -which is five miles away, but makes straight across the bush to B, -and strikes it exactly. How long did it take to go from A to B? - - -GAMBLING. - -197. Three friends, A, B, and C, sit down to play cards. As a result -of the first game, A lost to each of B and C as much money as they -started to play with; the result of the second game B lost similarly -to each of A and C; and in the third, C lost similarly to each of A -and B;--and they then had 24s. each. What had they each at first? - - -This Sticks Them Up. - -[Illustration] - -198. A, who is a dealer in horses, sells one to B for £55. B very -soon discovers that he does not require the animal, and sells him -back to A for £50. Now, A is not long in finding another customer for -the horse: he sells it to C for £60. How much money does A make out -of this transaction? - -This question has been the cause of endless discussion and argument. - -It might be as well to state that when A first sold the horse to B he -neither made nor lost any money by the deal. - - -SCRIPTURAL FINANCE. - -199. What is the earliest banking transaction mentioned in the Bible? -The answer generally given to this is, “The check which Pharaoh -received on the banks of the Red Sea, crossed by Moses & Co.” There -is still an earlier instance: see if you can find it out. - - -200. How much tea at 6s. per lb. must be mixed with 12 lbs. at 3s. 8d. -per lb. so that the mixture may be worth 4s. 4d. per lb.? - - -201. Place 17 little sticks--matches, for instance--making six equal -squares, as in the margin, then remove five sticks and leave three -perfect squares of the same size. - -[Illustration] - - -FOR THE JEWELLER. - -202. How much gold of 21 and 23 carats must be mixed with 30 oz of 20 -carats, so that the mixture may be 22 carats? - - -LONDON GRAMMAR. - -Three cockneys, being out one evening in a dense fog, came up to -a building that they thus described. The first said, “There’s a -_nouse_.” “No,” said the second, “It’s a _nut_.” The third exclaimed -“You’re both wrong; it’s a _nin_!” - - -203. A draper sold 12 yards of cloth at 20s. per yard, and lost 10 -per cent. What was the prime cost? - - -204. A jockey, on a horse galloping at the rate of 18 miles an hour -on the Flemington racecourse, passes in 30 minutes over the diameter -and curve of a semi-circle. What area does he enclose by the ride? - - -205. How many trees 20 feet apart cover an acre? - - “Multiplication is vexation, - Division is as bad. - The rule of three, it puzzles me, - And fractions drive me mad.” - - -MULTIPLY £19 19s. 11¾d. BY £19 19s. 11¾d. - -This very old question is continually cropping up, and will continue -to do so as long as men are able to reckon. The answer generally -given is £399 19s. 2d. and a fraction, and the method of working it -out as follows:-- - - £19 19s. 11¾d. = 19199 farthings. - - 19199 19199 368601601 - ----- x ----- = --------- and so on. - 960 960 921600 - -Many adopt the following method:-- - - £20 x £20 = £400 - - £ s d - 400 0 0 - ¼d x ¼d = 1/16 less 1/16 - ---------------- - £399 19 11-15/16 Ans. - -It would be possible to adopt other methods, each of which would give -a different result. - -Properly speaking, _this sum cannot be done_. - -Multiplication is merely a contracted form of addition: it means -taking a number or quantity a certain number of times. Every -multiplication can be proved by addition. All numbers are _abstract_ -or _concrete_--3 is abstract, £3 is concrete. - -Two abstract numbers can be multiplied together--as, 4 times 3 = 12. - - Proof: 3 - 3 - 3 - 3 - -- - 12 - -One abstract number and one concrete number can be multiplied -together--as 2s. multiplied by 3 = 6s. - - Proof: 2s. - 2s. - 2s. - --- - 6s. - -Two concrete numbers cannot be multiplied together. - -In the example just given, 2s. multiplied by 3, we see it simply -means to write down 2s. three times, and by addition we discover the -answer to be 6s. Suppose the reader lent a friend 2s. on Monday, 2s. -on Tuesday, and 2s. on Wednesday, he has lent 2s. three times, making -6s. lent in all. - -Now, we will attempt to multiply 2s. by 3s., but it is impossible -to comprehend how many times is 3s. times. The answer to 2s. x 3s. -usually given is 6s. On the same lines, we multiply 9d. by 10d., and -our answer is--90d., that is 7s. 6d.--a greater product than 2s. -multiplied by 3s. - -Although it is stated that two concrete numbers cannot be multiplied -together, it should be borne in mind that we can multiply yards, -feet, and inches, by yards, feet, and inches (length by breadth), -which will result in square or cubic measure: 12 inches make 1 foot, -and 3 feet make one yard, 144 square inches make 1 square foot, &c. -12 pence make 1 shilling, but how many square pence make 1 square -shilling? - -The argument generally brought forward in favour of the performance -of this problem is, that when the Rule of Three is applied to -financial questions (such as interests, &c.) money is multiplied by -money. - -Example.--If the interest on £10 is 15s., what is the interest on £20? - - As £10 : £20 :: 15s. : _x_ - - 15 - ____ - 10)300 - ---- - 30 Ans. 30s. - -The multiplication in the above is in appearance only, for all we get -in the Rule of Three is the ratio between the sums of money and this -ratio is an abstract number, and not concrete. On examination we find -the ratio between £10 and £20; that the latter is double, or _two_ -times as much as the former, and not £2 times more than it. - -We extend a general invitation to all our readers who hold a -different opinion to multiply three pints of Dewar’s Whisky by 6 -quarts of soda-water, but in case they might plead inability to -perform this little feat, on conscientious grounds, we will extend -the invitation to three cups of tea by six spoonfuls of sugar. And if -any of them have a few pounds (say £10) in the Savings Bank we would -advise “Don’t _add_ any more deposits, but wait till you have £2, -then proceed to the bank and multiply the £10 by the £2, and prove -to the teller that you have £20 to your account. Be careful to take -no less a sum than £2, or the result might be a little surprising, -for if you take only £1, the teller might argue after he has received -your sovereign that “ten ones are ten,” and then your £10 would -remain the same.” - - -206. What is the difference between six dozen dozen and half a dozen -dozen? - - -A TELL-TALE TABLE. - -There is a good deal of amusement in the following table. It will -enable you to tell how old the young ladies are. Ask a young lady to -tell you in which column or columns her age is found, add together -the figures at the top of the columns in which she says her age is, -and you have the secret. Suppose a young lady is 19. You will find -that number in the first, second and fifth columns; add the first -figures of these columns--1, 2 and 16--and you get the age. - - 1 2 4 8 16 32 - 3 3 5 9 17 33 - 5 6 6 10 18 34 - 7 7 7 11 19 35 - 9 10 12 12 20 36 - 11 11 13 13 21 37 - 13 14 14 14 22 38 - 15 15 15 15 23 39 - 17 18 20 24 24 40 - 19 19 21 25 25 41 - 21 22 22 26 26 42 - 23 23 23 27 27 43 - 25 26 28 28 28 44 - 27 27 29 29 29 45 - 29 30 30 30 30 46 - 31 31 31 31 31 47 - 33 34 36 40 48 48 - 35 35 37 41 49 49 - 37 38 38 42 50 50 - 39 39 39 43 51 51 - 41 42 44 44 52 52 - 43 43 45 45 53 53 - 45 46 46 46 54 54 - 47 47 47 47 55 55 - 49 50 52 56 56 56 - 51 51 53 57 57 57 - 53 54 54 58 58 58 - 55 55 55 59 59 59 - 57 58 60 60 60 60 - 59 59 61 61 61 61 - 61 62 62 62 62 62 - 63 63 63 63 63 63 - - -COIN PUZZLE. - -[Illustration: 2/-1d. 2/-1d. 2/-1d. 2/-1d.] - -207. Place four florins alternately with four pennies, and in four -moves, moving two adjacent coins each time, bring the florins -together and the pence together. When finished there must be no -spaces between the coins. - - -208. If 2 be added to the numerator of a certain fraction, it is made -equal to one-fifth, whilst if 2 be taken from the denominator it -becomes equal to one-sixth. Find the fraction. - - -EUCLID.--THE FAMOUS FORTY-SEVENTH. - -“_In any right-angled triangle, the square which is described -upon the side opposite to the right-angle is equal to the squares -described upon the sides which contain the right-angle._” - -Here is a simple way of proving this proposition. Although perhaps -not exactly scholastic, it is none the less interesting. - -Draw an exact square, whose sides measure 7 in.; then divide it into -49 square inches. Having done this, cut the figure in following the -big lines as shown by Fig 1. It will be observed that C is a complete -square, and that A and B will form a square: but as D is 1 in. short -of being a square, it is necessary to cut a square inch and add it on. - -[Illustration: Fig. 1.] - -[Illustration: Fig. 2.] - -Then construct a right-angled triangle as shown by Figure 2. - -We then see that the sum of the two small squares is equivalent to -the large square. - - D contains 9 small squares. - A & B do. 16 do. - -- - 25 - -And as we see that C has 25 small squares, it is thus proved that the -sum of the squares upon the sides which contain the right angle are -equal to the squares upon the side opposite the right angle. - -_Q.E.D._ - - -THE GREAT FISH PROBLEM. - -209. There is a fish the head of which is 9 in. long, the tail is as -long as the head and half the back, and the back is as long as the -head and tail together. What is the length of the fish? - - -210. How may 100 be expressed with four nines? - - -211. Two shepherds, A and B, meeting on the road, began talking of -the number of sheep each had, when A said to B, “Give me one of your -sheep, and I will have as many as you.” “Oh, no!” replied B; “give me -one of yours, and I will have as many again as you.” How many sheep -had each? - - -A BRICK PUZZLE. - -ONE FOR BUILDERS, CONTRACTORS, &C. - -212. Suppose the measurements of a brick to be:--Length, 9 in.; -breadth, 4½ in.; depth, 3 in. How many “stretchers, headers and -closures” can be cut out of one, and what would be the face area of -same? - -For the benefit of the uninitiated we might say that - - “stretcher” = length of brick x depth - “header” = breadth " - “closure” = half-breadth " - - -213. A woman has a basket of 150 eggs; for every 1½ goose egg she -has 2½ duck eggs and 3½ hen eggs. How many of each had she? - - -The Great Chess Problem. - -THE KNIGHT MOVE. - -214. Move the Knight over all the 64 squares of the chess board so -as to successively cover each square and, of course, not enter any -square twice. This problem has always proved to be an interesting -one. Mathematicians throughout all ages have devoted a good deal of -time to it. To chess players it should be especially attractive. - -[Illustration] - - -215. If 3 times a certain number be taken from 7 times the same -number the remainder will be 8. What is the number? - - -216. Divide £27 among 3 persons, A, B and C, so that B may have twice -as much as A, and C 3 times as much as B. - - -ANSWER THIS. - -217. Suppose it were possible for a man in Sydney to start on Sunday -noon, January 1st, and travel westward with the sun, so that it might -be in his meridian all the time, he would arrive at Sydney next day -at noon, Monday, Jan. 2nd. Now, it was Sunday noon when he started, -it was noon with him all the way round, and is Monday noon when he -returns. The question is, at what point did it change from Sunday to -Monday? - - -218. Start with 1 and keep on doubling for eight times, thus giving -nine numbers, and arrange them in a square that when multiplied -together, horizontally, vertically, or diagonally, the product of -each row will be the cube of the number which must go in the centre -of the square. - - -The happiest year in a man’s life is 40; for then he can XL. - - -Bound to Win! - -219. A certain gentleman, who was employed in one of our city -offices, purchased THE DOCTRINE OF CHANCE, which he studied -in his spare time, with the result that he sent in his resignation to -the head of the firm in order to try his luck on the racecourse. - -At the first meeting he attended, there were only three horses in a -race. His brother bookmakers were crying out the odds-- - -“Two to 1 bar one.” - -The odds on this latter horse which was “barred” he discovered to be -6 to 4 _on_. He determined to give far more liberal odds, and called -out-- - -“Even money, 2 to 1, and 3 to 1.” - -How could he give such odds, and yet win £1, _no matter which horse -wins the race_? - -[Illustration] - - -AN INCH OF RAIN. - -How many people really consider what is contained in the expression? -Calculated, it amounts to this:--An acre is equal to 6,272,640 square -inches; an inch deep of water on this area will be as many cubic -inches of water, which, at 277·274 inches to the gallon, is 22622·5 -gallons. The quantity weighs 226,225 lbs. Thus, an “inch of rain” is -over 100 tons of water to the acre. - - -Extract from a small boy’s first essay:--“Man has two hans. One is -the rite han an one is the left han. The rite han is fur ritin, and -the left han is fur leftin. Both hans at once is fur stummik ake.” - - -220. Find the side of a square whose area is equal to twice the sum -of its sides? - - -“THE EVIDENCE YOU NOW GIVE, &c., &c.” - -221. Smith, Brown, and Jones were witnesses in a law case. The -first-named gentleman swore that a certain thing occurred; Brown, on -being called, confirmed Smith’s statement, but Jones denied it. They -are known to tell the truth as follows:-- - - Smith, once in 3 times - Brown, " " 5 " - Jones, " " 10 " - -What is the probability that the statement is true? - - -When a man attains the age of 90 years, he may be termed -XC-dingly old. - - - - -Examination Gems. - - -A school examination room might not to a casual observer seem to be a -very likely place to find entertainment. However, the answers often -given by pupils are sometimes excruciatingly funny, as is proved by -the following:-- - - -DEFINITIONS. - -Function.--“When a fellow feels in a funk.” - -Quotation.--“The answer to a division sum.” - -Civil War.--“When each side gives way a little.” - -The Four Seasons.--“Pepper, mustard, salt and vinegar.” - -Alias.--“Means otherwise--he was tall, but she was alias.” - -Compurgation.--“When he was going to have anything done to him, and -if he could get anyone to say, ‘not innocent,’ he was let off.” - -The Equator.--“Means the sun. Suppose we draw a straight line and the -sun goes up to the top, then it is day, and when it comes down it is -night.” - -Precession.--“(1) When things happen before they take place. (2) The -arrival of the equator in the plane of the ecliptic before it is due.” - -Demagogue.--“A vessel that holds beer, wine, gin, whisky, or any -other intoxicating liquor.” - -Chimera.--“A thing used to take likenesses with.” - -Watershed.--“A place in which boats are stored in winter.” - -Gender.--“Is the way whereby we tell what sex a man is.” - -Cynical.--“A cynical lump of sugar is one pointed at the top.” - -Immaculate.--“State of those who have passed the entrance examination -at the University.” - -Frantic.--“Means wild. I picked up some frantic flowers.” - -Nutritious.--“Something to eat that aint got no taste to it.” - -Repugnant.--“One who repugs.” - -Memory.--“The thing you forget with.” - - -HISTORY. - -“Without the uses of History everything goes to the bottom. It is a -most interesting study when you know something about it.” - -“Oliver Cromwell was a man who was put into prison for his -interference in Ireland. When he was in prison he wrote ‘The -Pilgrim’s Progress,’ and married a lady called Mrs. O’Shea.” - -“Wolsey was a famous General who fought in the Crimean war, and who, -after being decapitated several times, said to Cromwell, ‘Ah, if I -had only served you as you have served me, I would not have been -deserted in my old age.’ He was the founder of the Wesleyan Chapel, -and was afterwards called Lord Wellington. A monument was erected to -him in Hyde Park, but it has been taken down lately.” - -“Perkin Warbeck raised a rebellion in the reign of Henry VIII. -He said he was the son of a Prince, but he was really the son of -respectable people.” - -Which do you consider the greater General, Cæsar or Hannibal? “If we -consider who Cæsar and Hannibal were, the age in which they lived, -and the kind of men they commanded, and then ask ourselves which was -the greater, we shall be obliged to reply in the affirmative.” - -Why was it that his great discovery was not properly appreciated -until after Columbus was dead? “Because he did not advertise.” - -What were the slaves and servants of the King called in England? -“Serfs, vassals, and vaselines.” - - -DIVINITY. - -Parable.--“A heavenly story with no earthly meaning.” - -“Esau was a man who wrote fables, and who sold the copyright to a -publisher for a bottle of potash.” - -What is Divine right? “The liberty to do what you like in church.” - -What is a Papal bull? “A sort of cow, only larger, and does not give -milk.” - -“Titus was a Roman Emperor, supposed to have written the Epistle to -the Hebrews. His other name was Oates.” - -Explain the difference between the religious belief of the Jews and -Samaritans? “The Jews believed in the synagogue, and had their Sunday -on a Saturday; but the Samaritans believed in the Church of England -and worshipped in groves of oak; therefore the Jews had no dealings -with the Samaritans.” - -Give two instances in the Bible where an animal spoke? “(1) Balaam’s -ass. (2) When the whale said unto Jonah, ‘Almost thou persuadest me -to be a Christian.’” - - -MATHEMATICS. - -A Problem.--“Something you can’t find out.” - -Hypotenuse.--“A certain thing is given to you, or it means let it be -granted that such and such a thing is equal or unequal to something -else.” - -“If there are no units in a number you have to fill it up with all -zeros.” - -“Units of any order are expressed by writing in the place of the -order.” - -“A factor is sometimes a faction.” - -“If fractions have a common denominator, find the difference in the -denominator.” - -“Interest on interest is confound interest.” - - -GRAMMAR. - -“Grammar is the way you speak in 9 different parts of speech; it is -an art divided in 4 quarters--tortology is one, and sintax one more.” - -An Abstract Noun.--“Something you can think of, but not touch--a -red-hot poker.” - -An Article.--“That wich begins words and sentences.” - -A Pronoun “is when you don’t want to say a noun, and so you say a -pronoun.” - -“A Adjective is the colour of a noun, a black dog is a adjective.” - -“Adjectives of more than one syllable are repaired by adding -some more syllables.” - -“Nouns are the names of everything that is common and has -a proper name.” - -Verb.--“To go for a swim is a verb what you do.” - -“Adverbs are verbs that end with a lie and distinguish words. It is -used to mortify a noun, and is a person, place, or thing, sometimes -it is turned into a noun and then becomes a noun or pronoun.” - -“Preposition means when you say anything of anything.” - -“Conjunction means what joins things together; ‘--and 2 men shook -hands.’” - -“Nouns denoting male and female and things without sex is neuter. -‘The cow jumped over the fence’ is a transitif nuter verb because -fence isen’t the name of anything and has no sex.” - -Interjection.--“Words which you use when you sing out.” - -“Gender is how you tell what sex a man is.” - - -Which Hand is It In? - -[Illustration] - -A person having in one hand a piece of gold, and in the other a piece -of silver, you may tell in which hand he has the gold, and in which -the silver, by the following method:-- - -Some even number (such as 8) must be given to the gold, and an odd -number (such as 3) must be given to the silver; after which, tell the -person to multiply the number in the right hand by any even number -whatever, and that in the left hand by an odd number; then bid him -add together the two products, and if the whole sum be odd, the gold -will be in the right hand and the silver in the left; if the sum be -even, the contrary will be the case. - -To conceal the artifice better, it will be sufficient to ask whether -the sum of the two products can be halved without a remainder--for in -that case the total will be even, and in the contrary case odd. - - -222. Which is the heavier, and by how much--a pound of gold or a -pound of feathers; an ounce of gold or an ounce of feathers? - - -223. Plant an orchard of 21 trees, so that there shall be 9 -straight rows with 5 trees in each row, the outline to be a regular -geometrical figure. - - -SETTLING UP. - -224. A person paid a debt of £5 with sovereigns and half-crowns. Now, -there were half the number of sovereigns that there were half-crowns. -How many were there of each? - - -A “CATCH.” - - | | | | | | | | | | | | | | | | | | | | - -225. How can you rub out 20 marks on a slate, have only five rubs, -and rub out every time an odd one? - - -226. From six take nine, from nine take ten, - From forty take fifty, and six will remain. - - -227. A man and his wife lived in wedlock, one-third of his age and -one-fourth of hers. Now, the man was eight years older than his wife -at marriage, and she survived him 20 years. How old were they when -married? - - -TO PROVE THAT YOU HAVE ELEVEN FINGERS. - -Count all the fingers of the two hands, then commence to count -backwards on one hand, saying, “10, 9, 8, 7, 6” (with emphasis on -the _6_), and hold up the other hand saying, “and 5 makes 11.” This -simple deception has often puzzled many. - - -228. A man travelled a certain journey at the rate of four miles an -hour, and returned at the rate of three miles an hour. He took 21 -hours in going and returning. What was the total distance gone over? - - -229. From what height above the earth will a person see one-third of -its surface? - - -230. The difference between 17/21 and 11/14 of a certain sum is £10. -What is the sum? - - -231. What decimal fraction is a second of a day? - - -232. Two trains are running on parallel lines in the same direction -at rates respectively 45 miles and 35 miles an hour; the length of -the first is 17 yds. 2 ft., and of the second 70 yds. 1 ft. How long -will the one be in passing the other? - - -233. - Suppose a bushel to be exactly round, - And the depth, when measured, eight inches be found; - If the breadth 18·789 inches you discover, - This bushel is legal all England over: - But a workman would make one of another frame, - Seven inches and a half the depth of the same; - Now say of what length must the diameter be, - That it may with the former in measure agree. - - -WORTH TRYING. - -A well known writer on mathematics, and a member of the Academy of -Science, Paris, says that the most skilful calculator could not in -less than a month find within a unit the cube root of -696536483318640035073641037. - - -A PROBLEM THAT WORRIED THE ANCIENTS. - -Many profound works have been written on the following famous -problem:-- - -“When a man says ‘I lie,’ does he lie, or does he not? If he lies he -speaks the truth; if he speaks the truth he lies.” - -Several philosophers studied themselves to death in vain attempts to -solve it. Reader, have a “go” at it. - - -THE CABINET MAKER’S PUZZLE. - -234. A cabinet maker has a circular piece of veneering with which he -has to veneer the tops of two oval stools; but it so happens that the -area of the stools, exclusive of the hand-holes in the centre and -that of the circular piece, are the same. How must he cut his veneer -so as to be exactly sufficient for his purpose? - - -THE ARITHMETICAL TRIANGLE. - - 1 - 2, 1 - 3, 3, 1 - 4, 6, 4, 1 - 5, 10, 10, 5, 1 - 6, 15, 20, 15, 6, 1 - 7, 21, 35, 35, 21, 7, 1 - 8, 28, 56, 70, 56, 28, 8, 1 - -Write down the numbers 1, 2, 3, &c., as far as you please in a -column. On the right hand of 2 place 1, add them together and place -3 under the 1; the 3 added to 3 = 6, which place under the 3, and -so on; this gives the second column. The third is found from the -second in a similar way. By the triangle we can determine how many -combinations can be made, taking any number at a time out of a larger -number. For instance, a group of 8 gentlemen agreed that they should -visit the Crystal Palace 3 at a time, and that the visits should be -continued daily as long as a different three could be selected. In -how many days were the possible combinations of 3 out of 8 completed? - -METHOD: Look down the first column till you come to 8, then -see what number is horizontal with it in the third column, viz., 56. -(For the method usually adopted for working out calculations like the -above, see DOCTRINE OF CHANCE.) - - -235. Why is a pound note more valuable than a sovereign? - - -KEEPING UP STYLE. - -236. A certain hotelkeeper was never at a loss to produce a large -appearance with small means. In the dining-room were three tables, -between which he could divide 21 bottles of wine, of which 7 only -were full, 7 half-full, and 7 apparently just emptied, and in such a -manner that each table had the same number of bottles and the same -quantity of wine. How did he manage it? - - -A DOMINO TRICK. - -Ask the company to arrange the whole set of dominoes whilst you are -absent in any way they please, subject, however, to domino rules--a -6 placed next to a 6, a 5 to a 5, and so on. You now return and -state that you can tell, without seeing them, what the numbers are -at either end of the chain. The secret lies in the fact that the -complete set of 28 dominoes, arranged as above-mentioned, forms a -circle or endless chain. If arranged in a line the two end numbers -will be found to be the same, and may be brought together, completing -the circle. You privately abstract one domino (not a double), thus -causing a break in the chain. The numbers left at the ends of the -line will then be the same as those of the “missing link” (say the -3-5 or 6-2.) The trick may be repeated, but you must not forget to -exchange the stolen domino for another. - - -237. A busman not having room in his stables for eight of his horses -increased his stable by one half, and then had room for eight more -than his whole number. How many horses had he? - - -AN ANCIENT QUESTION. - -238. “Tell us, illustrious Pythagoras how many pupils frequent thy -school?” “One-half,” replied the philosopher, “study mathematics, one -fourth natural philosophy, one-seventh observe silence, and there are -3 females besides.” How many had he? - - -EVADING THE QUESTION. - -239. A lady being asked her age, and not wishing to give a direct -answer, said, “I have nine children, and three years elapsed between -the birth of each of them. The eldest was born when I was 19 years -old, and the youngest now is exactly 19.” How old was she? - - -A ’CENTAGE “CATCH.” - -240. A man sells a diamond for £60; the number expressing the profit -per cent. is equal to half the number expressing the cost. What was -the cost? - - -241. Having 5½ hours to spare, how far may I go out by a coach at -the rate of 8 miles an hour so that I may be back in time, walking at -the rate of three miles an hour? - - -The Cross Puzzle. - -[Illustration] - -242. Cut out of a piece of card five pieces similar in shape and -proportion to the annexed figures. - - 1 piece similar to 1 - 3 pieces " " 2 - 1 piece " " 3 - -These five pieces are then to be so joined as to form a cross like -that represented by 4. - - -Irish Counting. - -An Irishman who had lately arrived in the colony was employed as -handy man at one of our large suburban mansions. The lady of the -house, hearing that some midnight thief had walked off with some of -her prize poultry, desired Pat to count them as speedily as possible -and to inform her how many there were; he accordingly left off -cleaning the buggy, and proceeded to enumerate the feathered bipeds. -The lady, getting impatient of waiting for him, repaired to the -poultry yard, and noticing him chasing a small chicken, enquired, -“Pat, whatever are you doing!” when the Irishman replied; “I’ve -counted all the chickens except this one; but the little varmint -won’t stand still till I count him.” - - -THE JEW “JEWED.” - -243. An old Jew took a diamond cross to a jeweller to have the -diamonds re-set, and fearing that the jeweller might be dishonest -he counted the diamonds, and found that they numbered 7 in three -different ways. Now, the jeweller stole two diamonds, but arranged -the remainder so that they counted 7 each way as before. How was it -done? - - 7 - 6 - 7 6 5 6 7 - 4 - 3 - 2 - 1 - - -244. A person wishing to enclose a piece of ground with palisades -found that if he set them a foot apart that he should have too few by -150, but if he set them a yard apart he should have too many by 70. -How many had he? - - -245. A mechanic is hired for 60 days on consideration that for each -day he works he shall receive 7s. 6d., but for each day he is idle he -shall pay 2s. 6d. for his board, and at the end he receives £6. How -many days did he work? - - -246. Take one from nineteen and leave twenty. - - -THE CAMEL PROBLEM. - -[Illustration] - -247. An Arab Sheik, when departing this life, left the whole of his -property to his three sons. The property consisted of 17 camels, and -in dividing it the following proportions were to be observed:-- - -The oldest son was to have one-half of the camels, the second son -one-third, and the youngest son one-ninth; but it was provided that -the camels were not, on any account, to be injured, but to be divided -as they were--living--between the three sons. - -Thereupon, a great argument ensued. The eldest son claimed 8½ -camels. The second insisted upon receiving 5⅔ of a camel; while -the youngest son would not be comforted with less than 1-8/9 of a -camel. The Cadi (or Judge) happened to appear on the scene. To him -the matter was explained. Without a moment’s hesitation he gave his -decision--a decision by which the claims of all three contestants -were fully satisfied. - -How did the Cadi settle this knotty question? - - -248. A grocer has 6 weights--each one twice as much as the one before -it in size. If he weighed the first five against the largest, it (the -largest) would only be 2 lbs. heavier than the combined weights of -the rest. What are the weights? - - -249. A squatter said to a new manager, whom he wished to test in -arithmetic: “I have as many pigs as I have cattle and horses, and -if I had twice as many horses I should then have as many horses as -cattle, and I should also have 13 more cattle and horses than pigs.” -How many of each had he? - - -250. A gentleman a garden had, five score[2] long and four score broad; - A walk of equal width half round he made, which took up half the - ground-- - You skilful in Geometry, tell us how wide the walk must be. - -[2] Feet. - - -251. Two boys, meeting at a farmhouse, had a mug of milk set down -to them; the one, being very thirsty, drank till he could see the -centre of the bottom of the mug; the other drank the rest. Now, if -we suppose that the milk cost 4½d., and that the mug measured 4 -inches diameter at the top and bottom, and 6 inches in depth, what -would each boy have to pay in proportion to the milk he drank? - - -Weight-for-Age Problem. - -252. There are 6 children seated at a table whose total ages amount -to 39 years. Tom, who is only half the age of Jack (the oldest) is -seated at the top, with Bob--who is a year older than him--next; -whilst Fred, who is four-fifths the age of Jack, is at the foot with -James, who is 1 year younger than Jack, next, him; the youngest, who -is a baby, is one-eighth the age of her brother Fred. Find the ages -of each, and weight of Fred, and by placing him third from the top -his initial and surname. You must express the ages in words, and use -the initial letters. - - -253. A flagstaff there was whose height I would know, - The sun shining clear straight to work I did go. - The length of the shadow, upon level ground, - Just sixty-five feet, when measured I found; - A pole I had there just five feet in length-- - The length of its shadow was four feet one-tenth - How high was the flagstaff I gladly would know; - And it is the thing you’re desired to show. - - -254. Put 4 figures together to equal 30, and the same figures to -equal 40. - - -255. A Salvation Army captain took up a collection, his lieutenant -took up another; if what the captain took up was squared and the -lieutenant’s added the sum would be 11d.; if what the lieutenant took -up was squared and the captain’s added the sum would be 7d. What was -the amount of the collection? - - -256. Find a number which, if multiplied by 17, gives a product -consisting only of 3’s. - - -THE “FOWL” PROBLEM. - -257. If a hen and a half lay an egg and a half in a day and a half, -how many eggs will 6 hens lay in 7 days? - - -258. Tom and Bill work 5 days each. Tom has as much and half as much -per day as Bill. The total amount of their wages for the 5 days is £1 -17s. 6d. What are their respective wages per day? - - -259. How many ¼ inch cubes can be cut out of a 2½ inch cube? - -260. - - miles. furl. po. yds. ft. in. - From 1 0 0 0 0 0 - Subtract 7 39 5 1 5 - ------------------------------ - - -THE SQUARE PUZZLE. - -[Illustration] - -261. A man has a square of land, out of which he reserves one-fourth -(as shown in the diagram) for himself. The remainder he wishes to -divide among his four sons so that each will have an equal share and -in similar shape with his brother. How can he divide it? - -Although this is a very old puzzle it is often the cause of much -amusement. - - -GENEROUS. - -262. A gentleman, having a certain number of shillings in his -possession, made up his mind to visit 17 different barracks and treat -the soldiers, and he did so in the following manner:--On going into -the first barracks, he gave the sentry one shilling and then spent -half of his shillings in the canteen amongst the soldiers, and on -coming out of barracks again he gave the sentry another shilling; -he repeated the same until he had finished with the seventeenth -barracks, and had no more shillings left. How many had he when he -commenced? - - -263. What part of 3 is a third part of 2? - - -264. Make 91 less by adding two figures to it. - - -265. If a church bell takes two seconds to strike the hour at 2 -o’clock, how many seconds will it take to strike 3 o’clock? - - -THIS CATCHES EVERYBODY. - -Ask a friend how many penny stamps make a dozen? He will reply, “Why, -twelve, of course.” Then ask again, “Well, how many half-penny ones?” -He is almost sure to reply, “Twenty-four.” - - -Before he settles his account with nature, man charges the debit -of his profit and loss account to Fate, but the credit he takes to -himself. - - -THE PUZZLE ABOUT THE “PROFITS.” - -Perhaps there is no form of commercial calculation so confusing -and so little understood as that of mercantile profits. It might -surprise many to state, nevertheless it is perfectly true, that it is -impossible to buy goods and sell them to show a profit as great as -100 per cent. - -The correct method to calculate profit is to reckon on the -_return_--the price received for the goods sold--_not on the cost -price_, and as it is impossible to sell goods at 100 per cent. -discount, so also goods cannot be sold to show that percentage of -profit, unless they actually cost nothing. - -Some time ago, in New Zealand, a well-known boot manufacturer had a -“GREAT DISCOUNT SALE.“ He had large posters displayed on the windows -of his shops, and advertisements in the newspapers, announcing the -fact that 5s. in the £ would be allowed as discount to all customers. -The profit he usually obtained in the ordinary way of trade was 25 -per cent., and having had a good season, he was prepared to sell off -the balance of his stock at cost price. The selling price of his -goods was marked in plain figures. A pair of boots which cost him 8s. -was marked 10s., thus showing a profit of 2s., which he considered to -be 25 per cent. (2s. being a quarter of 8s.) Instructions were issued -to all his employees engaged in selling to deduct a quarter from the -marked price, the result being that a pair of boots which cost 8s., -and marked 10s., was being sold at 7s. 6d. (2s. 6d., the quarter of -the marked price being deducted from 10s.) Although he imagined he -was getting 25 per cent. profit, he was in reality receiving only 20 -per cent. It was not long before the posters were altered, announcing -that 4s. in the £ would be allowed to his customers. - -The following question was asked some little time ago;--If a chemist -sold a bottle of medicine for 2s. 6d., which cost him 2½d., what -percentage would be his profit? - -Many work out the problem and answer 1100 per cent., but this answer -is incorrect. He received 2s. 6d. for that which cost him 2½d., -accordingly there was a profit of 2s. 3½d. We must now find out -what percentage is the latter amount of the selling price, 2s. 6d., -and we discover that it is 91⅔ per cent. - - -266. A pork butcher buys at auction £100 worth of bacon at 4d. per -lb. and sells it at 8d. per lb.; also £100 worth at 8d. per lb., -which he sells for 4d. per lb. Does he lose or gain? And if so how -much. - - -“THE JUMPING FROG.” - -267. A frog, sitting on one end of a log eight feet long, starts to -jump into a pond at the opposite end. With his first jump he clears -half the distance, the second jump half the remaining distance, and -so on. How many jumps does he take before entering the pond? - - -OBLONG PUZZLE. - -268. Cut out of a piece of cardboard fourteen pieces of the same -shape as those shown in the diagram--the same number of pieces as is -there represented--and then form an oblong with them. - -[Illustration] - - -269. If a man can load a cart in five minutes, and a friend can load -it in two and a half minutes, how long will it take them both to load -it, both working together? - - -270. A gentleman on being asked how old he was, said that if he did -not count Mondays and Thursdays he would be 35. What was his actual -age? - - -TOO SMART FOR DAD. - -“Pa,” said a boy from school, “How many peas are in a pint?” “How can -anybody tell that, foolish boy?” “I can every time. There is just one -‘p’ in pint the world over.” He was sent off to bed early. - - -SIMPLE PROPORTION. - -271. If it takes three minutes to boil one egg, how long will it take -to boil two? - - -“PUNCH’S” MONEY VAGARIES. - -The early Italians used cattle as a currency instead of coin (thus a -bull equals 5s.) and a person would send for change for a thousand -pound bullock, when he would receive 200 five pound sheep. If he -wanted _very_ small change there would be a few lambs amongst them. -The inconvenience of keeping a flock of sheep at one‘s bankers’, or -paying in a short-horned heifer to one’s private account led to the -introduction of _bullion_. - -As to the unhealthy custom of _sweating sovereigns_, it may be well -to recollect that Charles I., the earliest Sovereign, who was sweated -to such an extent that his immediate successor, Charles II., became -one of the lightest Sovereigns ever known in England. - -Formerly every gold watch weighed so many _carats_, from which it -became usual to call a silver watch a turnip. - -The Romans were in the habit of tossing their coins in the presence -of their legions, and if a piece of money went higher than the top of -their Ensign’s flag it was presumed to be “above the standard.” - - -“MARCH ON! MARCH ON!” - -272. An army 25 miles long starts on a journey of 50 miles, just as -an orderly at the rear starts to deliver a message to the General -in front. The orderly, travelling at a uniform speed, delivers his -message and returns to the rear, arriving just as the army finishes -the journey. How many miles does the orderly travel? - - -“WITH A LONG, LONG PULL.” - -[Illustration] - -273. If eight men are engaged in a tug-o’-war, four pulling against -four, on a continuous rope, and each man is exerting a force of -100 lbs., what strain is there at the centre of the rope? - - -“FIND OUT.” - -274. A gentleman in a train with a boy got into conversation with a -stranger, who asked him the lad’s age. The boy quickly replied, “This -gentleman, who is my uncle, is twice as old as me, but the sum of the -figures in my age are twice the sum of those in his.” What was the -age of each? - - -275. One of our squatters who had made his fortune in the “good -times” determined to sell his run and spend the rest of his days in -the old country. A new chum, possessing considerable wealth, and -desirous of settling down in Australia, hearing of the squatter’s -intention, interviewed him with the object of purchasing, when the -following conversation ensued:-- - -NEW CHUM: “How big is your run? What’s its area?” - -SQUATTER: “Well, I’m blessed if I know, but I can tell you -it’s perfectly square and enclosed with posts and rails. Each of the -rails is 9 ft. long.” - -NEW CHUM: “Oh, then, is it what you call a three-railed -paddock?” - -SQUATTER: “Yes, that’s so, and now I remember that _the -number of rails in my run is equal to the number of acres_. If you -like you can take a horse and ride round and count the rails, then -you will know the area.” This advice the new chum acted upon. - -Find out the length of his ride and the area of the run. - - -A Federal Problem. - -It is well known to our readers that paper money--such as pound -notes--issued in one colony are depreciated in another; thus a one -pound note of N.S.W. is only worth 19s. 6d. in Victoria, and _vice -versa_. Some time ago a rather ’cute individual in Wodonga, on the -Victorian side of the border, bought a drink in a local hotel with a -Victorian note, and received in change a N.S.W. note, which was worth -then and there only 19s. 6d.; he thereupon crossed the Murray to -Albury on the New South Wales side, bought another drink for sixpence -with his N.S.W. note, and received a Victorian note equal to 19s. -6d. in change. He travelled backwards and forwards during the day, -getting his twentieth and last drink in Albury, on the N.S.W. side, -whereupon he returns to Wodonga with a Victorian pound note still to -his credit. He thus paid for all his drinks, which amounted to ten -shillings. Who lost the money? - -We cannot advise readers to “go thou and do likewise,” for the simple -reason that such a proceeding would now be impossible, as exchange is -no longer charged in the two towns mentioned. It is not until we get -further from the border that the levy is made. - - -Doing Two Things at Once. - -An inspector was examining a school in a country district some -distance from a railway station. He was afraid of losing his train, -so hurrying with his work he tried to do two things at once. Standing -in the doorway, he gave out dictation to Class III. in the main room, -and at the same time gave out a sum to Class IV. in an adjoining -room, jerking out a few words alternately. - -The sum was “If a couple of fat ducks cost 19s., how many can he get -for £72 10s. 9d.” The dictation for Class III. began “Now as a lion -prowling about in search, &c.” Of course the poor children heard -both, and got a bit mixed. One little girl’s dictation began “Now a -couple of ducks prowling about in search of a lion who had lost 19s., -&c.” While a Class IV. lad was scratching his head over the following -sum “If 72 couples of fat lions cost 19s., how much prowling could be -got for £72 10s. 9d.” - - -TWO CALENDAR CATCHES. - -Ask a person if Christmas Day and New Year’s Day come in the same -year. The answer generally given is “Of course not, Christmas comes -in this year, and New Year’s Day in the next.” - -Another question that often puzzles many. Have we had more Christmas -days than Good Fridays? The usual answer is “No, both the same.” - -276. A brass memorial tablet in honour of the late Sir Charles Lilley -has been fixed in the centre of the eastern wall of the Brisbane -Grammar School Hall. The enthusiasm displayed by Sir Charles in -the cause of education generally, and his work on behalf of the -Grammar School, make this commemoration particularly appropriate. -The following is the inscription, to translate which should prove a -capital exercise to all Latin scholars. The tablet measures 50 inches -by 30 inches. - -[Illustration: MEMORIAL TABLET TO THE LATE SIR CHARLES LILLEY] - -It may be added that the lettering of the plate was designed by Mr. -R. S. Dods, architect, and the engraving was done in Brisbane by -Messrs. Randle Bros., the well-known engravers, of Elizabeth Street. - - -A Puzzle in Book-keeping. - -277. A firm appointed an agent to do business on their account, and -gave him £32 17s. in cash for expenses, &c., and also supplied him -with a stock of goods, the value wholesale being £57 14s.; while in a -distant town he bought a job lot of goods for £59 19s., which he paid -cash for out of what he had realised on his first stock. He still -continued to sell, but very soon after the firm called him in, and -desired him to close his account and hand in a full statement. - -His total retail sales amounted to £102 17s., and he returned goods -to the value of £31 17s., his expenses had been £25. - -Question--What does the firm owe the agent, or the agent owe the firm? - -THE AGENT’S STATEMENT BEING-- - - Cash £32 17 - Goods 57 14 - Paid for Goods 59 19 - Cash Sales 102 17 - Goods Returned 31 17 - Expenses 25 0 - -This puzzle first appeared in “HOW TO BECOME QUICK AT -FIGURES,” the answer being withheld. It is a record of -transactions that actually occurred in America, which were the -subject of litigation. Although we received thousands of replies, -not more than 5 per cent. were correct. It is a question that -individuals not conversant with book-keeping would be as likely to -solve correctly as the expert. For the convenience of those who are -unacquainted with American money we have been obliged to substitute -£ s. d., and would advise our readers to attempt a solution before -referring to the answer. - - - - -CONCLUSION. - - -In bringing “THE PUZZLE KING” to a conclusion, the author -can only express the hope that he has been successful in his -endeavour to make it not only an amusing work but also a _useful_ one. - -The impossibility of making a book of this nature perfect is fully -recognised, and corrections or contributions will be cordially -received, and the contributor liberally remunerated. - -All communications must be sent to 44 Pitt Street, Sydney, addressed -to the author, who tenders to all readers of “THE PUZZLE -KING”-- - - AN ARITHMETICAL TOAST. - “Here’s an _addition_ to your wages. - Here’s a _subtraction_ from your wants and miseries. - Here’s a _multiplication_ of your joys and happiness. - Here’s a _division_ amongst your enemies. - Here’s a _reduction_ of your hours of labour. - And here’s a hope that you’ll all be able to _practice_ - and take _interest_ in “THE PUZZLE KING.” - - - - -Answers. - - -(1) 12,111. - -(2) 24s. - -(3) 18. - -(4) He lost £13 6s. 8d. - -(5) - - +-----+-----+-----+-----+ - | 485 | 463 | 475 | 465 | - +-----+-----+-----+-----+ - | 461 | 467 | 487 | 473 | - +-----+-----+-----+-----+ - | 483 | 477 | 457 | 471 | - +-----+-----+-----+-----+ - | 459 | 481 | 469 | 479 | - +-----+-----+-----+-----+ - -(6) See No. 225. - -(7) £30. - -(8) 675 springs. - -(9) [Illustration] - -(10) - - Suppose a man and woman to marry, the man to have - had a son by a former marriage (the gentleman who - leaves the money); also the woman has a daughter - by a former marriage. This son and daughter get - married, and have a son. This is the scheme of - kindred, and answers the conditions of the paradox. - -(11) 4d. There were three of them--grandfather, father, and son. - -(12) The total score was 240. The 1st player scored 30; - the 2nd and 3rd, 24 each; the 4th, 5th, and 6th, 12 - each; the 7th, 8th, 9th, and 10th, 30 each; and the - 11th, 6. - -(13) They tip the pail over horizontally; if any part of - the bottom can be seen without spilling the milk it - is not half full. - -(14) In 9-68/78 days. - -(15) The measurements given would not make a triangle. - -(16) 6400 soldiers. - -(17) [Illustration] - -(18) The LEFT BOWER. - -(19) - - The first £15 - " second 8 - " third 10 - " fourth 6 - --- - The man had £39 - -(20) The first boat 15 min. 45 secs., the second 16 min. - -(21) 3 animals. - -(22) A comma. - -(23) 15 and 10. - -(24) 21 and 54. - -(25) 126. - -(26) 72 persons. - -(27) 20·7846 inches; 203·646 square inches. - -(28) - 11 plus 1·1 = 12·1 - 11 x 1·1 = 12·1 - -(29) Coach fare 3s. - -(30) The distance from the ends of the least side on the - largest and intermediate sides are respectively - 211⅓ and 176 links. - -(31) 60. - -(32) T wins--distance 90 miles; walking pace--T 5 miles per hour, D 4. - -(33) - - +---+---+---+---+---+---+---+---+---+ - | A | B | C | D | E | F | G | H | I | - +---+---+---+---+---+---+---+---+---+ - - My friends,--I have spare blankets, and I shall need no more; - The tenth man can have my bed, and I’ll sleep on the floor. - In room marked A two men were placed; the third was lodged in B; - The fourth to C was then assigned, the fifth retired to D; - In E the sixth he tucked away, in F the seventh man, - The eighth and ninth in G and H, and then to A he ran - (Wherein the host, as I have said, had laid two travellers by); - Then taking one--the tenth and last--he lodged him safe in I: - Nine spare rooms--a room for each--were made to serve for ten. - And this it is that puzzles me and many wiser men. - -(34) £78 7s. 0·42d. - -(35) 275625 leaves. - -(36) [Illustration: _Fig 1_] - -(37) 24000 men. - -(38) 4032 lines. - -(39) 28·9 miles. - -(40) £26 7s. 7d. - -(41) 7 and 1. - -(42) - - +----------------------------+ - | 47 58 69 80 1 12 23 34 45 | - | 57 68 79 9 11 22 33 44 46 | - | 67 78 8 10 21 32 43 54 56 | - | 77 7 18 20 31 42 53 55 66 | - | 6 17 19 30 41 52 63 65 76 | - | 16 27 29 40 51 62 64 75 5 | - | 26 28 39 50 61 72 74 4 15 | - | 36 38 49 60 71 73 3 14 25 | - | 37 48 59 70 81 2 13 24 35 | - +----------------------------+ - -(43) - - 8 3 4 - 1 5 9 - 6 7 2 - -(44) Don’t be A flat be A sharp. - -(45) £49. - -(46) - - +-----------+ - | 3 3 3 | - | | - | 3 3 | - | | - | 3 3 3 | - +-----------+ - - +-----------+ - | 4 1 4 | - | | - | 1 1 | - | | - | 4 1 4 | - +-----------+ - -(47) Give the last person an egg on the dish. - -(48) 20 lbs. - -(49) 1 wether, 10 ewes, 9 lambs. - -(50) 15 hours. - -(51) 12 square miles. - -(52) 7 persons. - -(53) The versed sine of the segment of Will’s cake which - was given to Jack was 3·05 inches, and its area - 26·0058364375 square inches: hence Will’s share - was 704·6125135625 square inches, and Jack’s share - 704·5914364375 square inches; so that Will’s four - were about 52·03275 square inches more than Jack’s - six, and Will, of course, lost the wager. After the - decision of the gauger, Will’s share was ·0210771245 - (1-50th nearly) of a square inch more than Jack’s. - -(54) 8·46851 seconds velocity, 129·38 ft. per second. - -(55) 144 minutes. - -(56) - - 39 - 12 - ----- - 78 - 39 - ----- - 468 - -(57) 8835 yds. - -(58) 2513·28 sq. yds nearly. - -(59) A 13 times, B 8. - -(60) Her son. - -(61) 3 wickets. - -(62) Not fully stated--suppose 4 miles per hour. - -(63) 22 plus 2 eq. 24; 3^3-3 eq. 24. - -(64) 1s. 11d. or 11s. 1d. - -(65) TOBACCO. - -(66) 1 ft. 5·6268 inches. - -(67) [Illustration] - -(68) Age 28. - -(69) 8/9 - -(70) [Illustration: 1 2 3 4 5 6 7 8 9 10] - -4 on 1, 6 on 9, 8 on 3, 5 on 2, and 10 on 7. - -(71) They put one plank across the angle; the end of the - other resting on it will reach the island. - -(72) 283; 224. - -(73) 23; 24. - -(74) Gallons 1207·45, diameter 6 ft., height 6 ft, 10¼ in. - -(75) 76; 24. - -(76) One travels West and the other East going round the - world once a year; one will gain one day per annum, - and the other will lose a day. In 50 years the - difference will amount to 100 days. - -(77) Diameter 87032 miles, circumference 273529 miles, -area 23805775928 miles. - -(78) - - +-----+-----+-----+ - | 621 | 642 | 627 | - | | | | - | 636 | 630 | 624 | - | | | | - | 633 | 618 | 639 | - +-----+-----+-----+ - -(79) The two ends of the box are placed so that they lap - over the two sides, and the wood being one inch - thick the length is thus increased by 2 inches. - -(80) 96s. - -(81) First £25 5s., second £28 5s., third £30 5s., fourth - £36 5s. - -(82) [Illustration] - -(83) (5-5/5)·5. - -(84) 10 inches. - -(85) 5 miles 1300 yds. - -(86) £10. - -(87) 10, 22, 26. - -(88) - - 987654321 = 45 555555555 = 45 - 123456789 = 45 or 99999 = 45 - --------- --------- - 864197532 = 45 555455556 = 45 - -(89) - - The 1st part 8 add 2 = 10 - " 2nd " 12 subtract 2 = 10 - " 3rd " 5 multiply by 2 = 10 - " 4th " 20 divide by 2 = 10 - ---- - 45 - -(90) - - 3025. 30 plus 25 = 55 which squared is 3025 - 9801. 98 plus 01 = 99 which squared is 9801 - -(91) 3 children. - -(92) 36 inches. - -(93) The difficulty is to determine what would have been - the will of the testator had he foreseen that his - wife would be delivered of twins. As he desired that - in case his wife brought forth a son he should have - ⅔ of his property, and the mother ⅓, it follows - that his intention was to give his son a sum double - to that of the mother; and as he desired in the - other case that if she brought forth a daughter the - mother should have ⅔ and the daughter ⅓, there - is reason to conclude that he intended the share - of the mother to be double that of the daughter; - consequently, to unite these two conditions, the - heritage must be divided in such a manner that the - son may have twice as much as the mother, and the - mother twice as much as the daughter. Thus we get-- - - Son’s share, £4000 - Mother’s " £2000 - Daughter’s " £1000 - - Sometimes the following difficulty is proposed in regard - to this problem:--In case the mother should have - two sons and one daughter, in what manner must - the property be divided then? We refer you to the - lawyers. - -(94) 23 years 289 days--a little less than 24 years. - -(95) [Illustration] - -(96) 1650 ft. deep; 1½ minutes. - -(97) [Illustration] - -(98) - - Man, 69 yrs 12 weeks - Woman, 30 yrs 40 weeks - -(99) A 18 hours, B 22½. - -(100) 3 and 2. - -(101) 12 pence. - -(102) 50s. - -(103) - - It is used so in the question. The answer generally - given is found in the Bible (Judges xvi, 7 and 8). - Samson was bound with “seven green withs.” - -(104) - - 32 or 46 or 95-72/36 or 14 - 57 35 1-8/4 76 - --- --------- - 89 17 100 5 - --- - 1 98 3 - --- - 6 2 98 - --- - 4 100 2 - --- --- - 100 100 - -(105) - - 56 or 20 or 40 - 24 8 36 - --- - 80 7 15 - 1 35 7 - 9 46 98 - 3 19 2 - --- --- - 7 100 100 - --- - 100 - -(106) 44 feet. - -(107) 8 persons. - -(108) 8¼. - -(109) The stone should fall into his hand. - -(110) 6⅗ days. - -(111) £5 8s. 6d. - -(112) TEN - -(113) - - To explain this often causes much confusion. We - must take a simple illustration: I have a garden - containing 10 appletrees, all bearing fruit. Now, - there are more trees than any tree has apples on - it; there must be at least 2 trees having the same - number of apples--for instance, if No. 1 tree has - 1 apple, No. 2 has 2, and so on to No. 9; when we - come to No. 10 tree, it must have the same as one - of the other trees, as it could not have 10 or more - according to our first supposition. - -(114) It simply means that _four_ “nothings” equal -_one_ “nothing.” - -(115) He had a half-penny, and he borrowed a half-penny. - -(116) 5. - -(117) 30 apples. - -(118) 18 and 27. - -(119) - - A 3240 - B 2916 - C 1944 - D 2052 - E 1728 - Electors 6480. - -(120) - - A £12 - B £20 - C £30 - -(121) 45 miles. - -(122) 80, 60, 45. - -(123) £580. - -(124) Hendrick and Anna. Claas and Catrün. Cornelius and Gertruig. - -(125) - - A 2304 - B 1296 - -(126) £19,005. - -(127) 15 days. - -(128) - - 1st £2180 3s. 4¼d. - 2nd £2380 15s. 11¼d. - 3rd £2599 17s. 9¾d. - 4th £2839 2s. 10¾d. - -(129) 1-2/18 minutes. - -(130) 36 pyramids. - -(131) 82·076 feet. - -(132) 55-5/5 = 56 = 4 x 4 plus 40. - -(133) 6 women. 10⅞d. per yard. - -(134) A 21. B 28. Youngest child 7. - -(135) - - We see that each of the members present paid 4d. - to make up 5s. There must have been 15 persons - present when the bill was paid, and consequently 18 - at dinner. Now, it is evident that the classes are - as 2, 3, and 4, making 4 Officers, 6 Non-com’s, - and 8 Privates. Again, it is evident that 5s. being - the sum to be paid by 1 Com. and 2 Non-coms.; each - Com.’s share was 2s., and each Non-com’s 1s. - 6d., and from the conditions of the question each - Private’s share was 1s. 3d.; those who remained had - to pay. - 3 Officers, 2s. each and 4d. each 7s. 0d. - 4 Non-coms, 1s. 6d. each " 7s. 4d. - 8 Privates, 1s. 3d. " " 12s. 8d. - ----------- - Amount £1 7s. 0d. - -(136) The Alphabet. - -(137) 4 glasses. - -(138) 37·6992 feet. - -(139) 157-1/7 square miles. - -(140) 324. - -(141) Bottle 2¼d., cork ¼d. - -(142) 1, 4, 16, and 64. - -(143) 16 days. - -(144) 7¼d., 4¾d. - -(145) 1st, 64; 2nd, 48; 3rd, 36; 4th, 27 gals. - -(146) 1st £24, 2nd £20, 3rd £8, 4th £28. - -(147) - - This is one of those _impossible_ questions that - one often hears. The fractions, when added together, - equal 19/20. So the whole £1 _cannot be so divided_. - The following solution is often put forward:-- - - ⅓ plus ¼ plus ⅕ plus ⅙ = 20 plus 15 plus 12 plus 10 = 57 - -------------------------- -- - 60 60 - s. - 20 x 20 = 400 div. 57 = 7-1/57 to 1st son - 15 x 20 = 300 div. 57 = 5-15/57 " 2nd " - 12 x 20 = 240 div. 57 = 4-12/57 " 3rd " - 10 x 20 = 200 div. 57 = 3-29/57 " 4th " - -------- - 20s. - -(148) - The locomotive pushes No. 1 truck up to the points, - then returns to the opposite siding and pushes No. 2 - up to No. 1 at the points; the two trucks are then - pulled by the locomotive down the siding and pushed - on to the main line to a position anywhere between - the two sidings; No. 1 is then uncoupled and left - standing, whilst the locomotive pulls No. 2 along - the main line in order to push it up to the points - where it is left; the locomotive returns to No. 1, - and pulling it a short distance, in order to get - on the proper siding, pushes it into its required - position, uncouples, and proceeds up the other - siding to the points to pull No. 2 into its proper - place, then uncouples and returns to the main line. - -(149) 14,400 quarts - -(150) A, 2s. 7½d.; B, 1s. 1½d.; C, 9d. - -(151) - - 1st Company, £2400 - 2nd " 1800 - 3rd " 1600 - 4th " 1500 - ----- - £7300 - -(152) Lines, 29; letters, 32. - -(153) Major £100, minor £60. - -(154) From A £88, from B £44. - -(155) [Illustration] - -(156) 25 miles from Sydney. - -(157) 4½ miles. - -(158) 108. - -(159) - - Two-thirds of SIX is IX; the upper half of XII is VII; - The half of FIVE is IV; and the upper half of XI is VI. - -(160) £12 12s. 8d. = 12128 farthings. - -(161) J £660, M £440, B £220. - -(162) Masons 20s., Bricklayers 15s., Laborers 10s. - -(163) £29 19s. 9¼d. - -(164) 2 years. - -(165) [Illustration] - -This draught puzzle can also be done in three other ways. - -(166) - - Wife £4650 - Son 6200 - Eldest daughter 3100 - Youngest " 1550 - ------ - Total £15,500 - -(167) [Illustration] - -(168) 18. - -(169) 6¼ per cent. - -(170) - 19 movements - 19 feet - -(171) 895 and 11,277. - -(172) 56 quarts. - -(173) 20; 50 gals. - -(174) 117 ft. 9 in. - -(175) 1st 1¼d., 2nd ¾d. - -(176) - - The lazy sundowner 2 days at 2 hours per day = 4 hours - " second " 4 " " 4 " " " = 16 " - " third " 6 " " 6 " " " = 36 " - " fourth " 12 " " 12 " " " = 144 " - -------- - 200 hours - -(177) 17777873. - -(178) - The “catch” is in the word _ears_; he carries - out two ears on his head and one ear of corn each - day--hence it will take 6 days. - -(179) My daughter. - -(180) Man 3s., boy 2s. - -(181) 11·9. - -(182) 72 gals. - -(183) - The landlord would lose by such an arrangement, as - the rent would entitle him to 2/5 of the 18; the - selector should give him 18 bushels from his own - share after the division is completed. - -(184) £1 6s. 8d., £1 13s. 4d. - -(185) 3.362 inches. - -(186) The merchant, 1d. - -(187) - - Train from London 44 miles per hour - " " Edinburgh 53-7/9 " " " - -(188) - A gentleman and one servant go over; the gentleman - returns with the boat, 2 servants go over; 1 servant - returns; 2 gentlemen go over; 1 gentleman and 1 - servant return; 2 gentlemen go over; 1 servant - returns; 2 servants go over; 1 servant returns; the - two servants then go over. - -(189) - - Imperfect. (Sample of questions we receive daily. - Give it to your friends: it will annoy them.) - -(190) 14, 112, 378, 896. - -(191) 120 lbs. - -(192) 80 years. - -(193) 6-6/6. - -(194) 13 trains. - -(195) Distance, 12½ miles; rate, 8 miles per hour. - -(196) 5½ hours. - -(197) A 39s., B 21s., C 12s. - -(198) £10. - -(199) When Pharaoh’s daughter drew a little prophet (profit) - from the banks of the Nile. - -(200) 4⅘lbs. - -(201) [Illustration] - -(202) 30 oz. of 21, 90 oz. of 23. - -(203) £1 2s. 2⅔d. - -(204) 3078 ac. 3r. 2·88p. - -(205) 108 trees. - -(206) 792. - -(207) [Illustration] - -(208) 8/50. - -(209) 72 inches. - -(210) 99-9/9. - -(211) A 5, B 7. - -THE BRICK PUZZLE. - -(212) 2 stretchers, 4 headers, 4 closures. Area, 135 inches. - -This question has been the cause of much discussion, especially -amongst those engaged in the building trade. - -[Illustration: Fig. 1--Represents the brick and the method of -cutting it.] - -[Illustration: Fig. 2--Represents the face of the wall showing the -area of brick when cut. It has been necessary to produce this figure -on half-scale to that of Fig. 1.] - -(213) Goose 30, duck 50, hen 70. - -THE KNIGHT MOVE. - -(214) It does not matter on which square the knight is first placed, -his last square to enter will be at a knight’s distance from the -first. The route may be varied in many ways. - -[Illustration] - -(215) 2. - -(216) A £3, B £6, C £18. - -(217) Cannot be answered. - -(218) - - +------+------+------+ - | | | | - | 8 | 256 | 2 | - | | | | - +------+------+------+ - | | | | - | 4 | 16 | 64 | - | | | | - +------+------+------+ - | | | | - | 128 | 1 | 32 | - | | | | - +------+------+------+ - -(219) - - Even, £6 against £6--£12 - 2 to 1, £8 against £4--£12 - 3 to 1, £9 against £3--£12 - -- - £13 Received. - -Whichever horse wins, he must pay £12, and has received -£13 to pay with. - -(220) 8. - -(221) 9 to 8 _on_. - -(222) 1 lb. of feathers by 1240 grains; 1 oz. of gold by 42·5 grains. - -(223) [Illustration] - -(224) Sovereigns, 4; half-crowns, 8. - -(225) - Count backwards, saying 20, 19, 18, 17, with - emphasis on the _17_, remarking “That’s odd, isn’t - it?” The reply will be “Yes.” Proceed in that manner - throughout. This question and No. 6, although not - the best of “catches,” are often asked. - -(226) - - SIX IX XL - IX X L - ----------- - S I X - -(227) Man 24, woman 16. - -(228) 72 miles. - -(229) The diameter of the earth. - -(230) £420. - -(231) ·000011574. - -(232) 18 seconds. - -(233) 19·405 inches. - -(234) [Illustration] - - He must cut the piece of veneer as shown by the middle - figure, when he will be able to get his two ovals. - -(235) - Because you double it when you put it in your - pocket, and you see it in creases (increases) when - you take it out. - -(236) He did this in two ways;-- - - _Table_ Full. Half-full. Empty. - 1 | 2 3 2 - 2 | 2 3 2 - 3 | 3 1 3 - --------+---------------------------- - 1 | 3 1 3 - 2 | 3 1 3 - 3 | 1 5 1 - -(242) [Illustration] - -(243) - - 7 - 7 6 7 - 5 - 4 - 3 - 2 - 1 - -(244) 180. - -(245) Worked 27 days, idle 33. - -(246) XIX, take away I, leaves XX. - -(247) - The Cadi added his camel to the 17, thus making - 18 in all; then the oldest son received 9, second - son 6, youngest 2. He then took his own camel, and, - departing, left the sons quite satisfied. - -(248) 2, 4, 8, 16, 32, 64 lbs. - -(249) 13 horses, 26 cattle, 39 pigs. - -(250) 12 ft. 11⅞ in. - -(251) - - 1st boy, 14·18 farthings - 2nd " 3·82 " - -(252) - - Jack, 10 yrs. Tom =FIVE= Tom =F=ive - James, 9 " Bob =S=ix Bob =S=ix - Fred, 8 " Jack =T=en Fred =E=ight - Bob, 6 " Baby =O=ne Jack =T=en - Tom, 5 " James =N=ine Baby =O=ne - Baby, 1 " Fred =E=ight James =N=ine - -(253) 79·26 feet. - -(254) 9 plus 9 plus 9 plus 3 = 30, 39-9/9 = 40, -or 28-2/1 = 30, 28 plus 12 = 40. - -(255) 5d. - -(256) 196078431372549. Method: Keep on adding imaginary -3’s until it comes out thus--17)33/17(196078431372549 - - To prove it:-- 196078431372549 - 17 - ---------------- - Proof-- 3333333333333333 - -(257) - - 28 eggs. Method: 1½ hens lay 1½ eggs in 1½ days - 1½ " " 3 " " 3 " - 3 " " 6 " " 3 " - 3 " " 2 " " 1 " - 6 " " 4 " " 1 " - 6 " " 28 " " 7 " - -(258) Tom, 4s. 6d. per day; Bill, 3s. - -(259) 1000. - -(260) 1 inch remainder. - -(261) [Illustration] - -(262) 393,213 shillings. - -(263) 2/9. - -(264) 9½. - -(265) 4 seconds. - -(266) Loses £50. - -(267) He will never enter the water, because the frog’s - jump, at any time, is only half-way to the water. - -(268) [Illustration] - -(269) 1⅔ minutes. - -(270) 49 years. - -(271) 3 minutes. - -(272) - - | | | | | - -----------+----------+-----+-----+-- - A B C D E - - Let A be starting point of Orderly; B be starting point - of General; C be point at which Orderly returns - to his place, the rear having marched 50 miles to - this point; D be point at which Orderly delivers - his despatches; E be destination of front rank or - General of Army. - - Let _x_ eq. number of miles between C and D. - - Then AD eq. (50 plus _x_) miles; BD eq. (25 plus _x_) - miles; DE eq. (25 minus _x_) miles; and AD plus DC - eq. (50 plus 2_x_) miles, and is the total distance - the Orderly travels. - - Now Orderly rides from A to D, while General marches - from B to D, and Orderly returns from D to C, while - General marches from D to E, and Orderly and Army - travel at a uniform rate. - - ∴ AD : BD :: DC : DE - or 50 plus _x_ : 25 plus _x_ :: _x_ : 25-_x_ - ∴ 1250-25_x_-_x_^2 eq. 25_x_ plus _x_^2 - Whence _x_ eq. 15.45 plus. - ∴ Orderly rides 50 plus 30.9 plus - eq. 80.9 plus - eq. 80 miles 1587 yards nearly. - -(273) 400 lbs. - -(274) Gentleman 30, boy 15. - -(275) Ride, 44 miles; area, 77,440 acres. - -(276) - Translation: The foundation stone of this - building was laid in 1880 by Sir Charles Lilley, - for many years Chief Justice, and formerly a - distinguished member of the Government of this - colony. He was prominent amongst those who worked - for the first establishment of this school, and - afterwards, by his generous gifts and by his wise - counsel as a trustee, contributed greatly to its - advancement. The trustees have, therefore, erected - this tablet to perpetuate his memory here. A.D. 1898. - -(277) The agent owes the firm £7 19s. - -DIDDAMS PRINTER, BRISBANE. - - - - - -End of the Project Gutenberg EBook of The Puzzle King, by John Scott - -*** END OF THIS PROJECT GUTENBERG EBOOK THE PUZZLE KING *** - -***** This file should be named 52052-0.txt or 52052-0.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/5/2/0/5/52052/ - -Produced by MWS, Paul Marshall and the Online Distributed -Proofreading Team at http://www.pgdp.net (This file was -produced from images generously made available by The -Internet Archive) - - -Updated editions will replace the previous one--the old editions will -be renamed. - -Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the United -States without permission and without paying copyright -royalties. 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