Part 33

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.

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.

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?