Part 9
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.
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.
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.”
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.
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.