Part 9
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.”
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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]