Part 2
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.