John Scott

“ 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.” ”

“ 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. ”

“ 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? ”

“ 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%. ”

“ 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% ”

“ Suppose that the world always did and always will contain 990,000,000 inhabitants, and that a generation lasts 331⁄3 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. ”

“ 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! ”

“ 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? ”

“ 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. ”

“ 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 ”

“ 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? ”

“ Everyone seems to over-estimate the proper height.
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. ”

“ 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. ”

“ 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. ”

“ 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.
COIN PUZZLE.
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. ”

“ 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. ”

“ 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.
94.
Money lent at 6 per cent To those who choose to borrow ”

“ 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 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. ”

“ 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.” ”

“ 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 ”

“ 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. ”

“ 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? ”

“ 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. ”

“ Question—What does the firm owe the agent, or the agent owe the firm?
The Agent’s Statement Being—
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. ”

“ 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. ”

“ 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 ”

“ 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? ”

“ 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. ”

“ 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. ”

“ 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. [Pg 99]
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. ”

“ 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 21⁄4 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. ”

“ 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. ”

“ 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. ”

“ 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. ”

“ 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?” [Pg 23]
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 ”

“ 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. ”

“ 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. ”

“ 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? [Pg 26]
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. ”