Part 3

At a large manufactory a patent pump refused to work. Several engineers failed to discover the cause. The local plumber, however, succeeded, after a few minutes, in putting it in working order, and sent to the company--

To Mending pump 2 0 " Knowing how 5 0 0 ------ Total £5 2 0

A VETERINARY SURGEON’S ACCOUNT.

To curing your pony, that died yesterday, £1 1s.

3. What is the number that the square of its half is equal to the number reversed?

HOW TO GET A HEAD-ACHE.

Naturalists state that snakes, when in danger, have been known to swallow each other; the above three snakes have just commenced to perform this operation. The snakes are from the same “hatch,” and are therefore equal in age, length, weight, &c. They all start at scratch--that is, commence swallowing simultaneously. They are twirling round at the express rate of 300 revolutions per minute, during which time the circumference is decreased by 1 inch.

We would like our readers to tell us what will be the final result? Heads or tails, and how many of each?

4. A man sold two horses for £100 each; he lost 25 per cent. on one, and gained 25 per cent. on the other. Was he “quits”; or did he lose or gain by the transaction; and, if so, how much?

A GOOD CARD TRICK.

The performer lays upon the table ten cards, side by side, face downwards. Anyone is then at liberty (the performer meanwhile retiring from the room) to shift any number of the cards (from one to nine inclusive) from the right hand end of the row to the left, but retaining the order of the cards so shifted. The performer, on his return, makes a little speech: “Ladies and gentlemen, you have shifted a certain number of these cards. Now, I don’t intend to ask you a single question. By a simple mental calculation I can ascertain the number you have moved, and by my clairvoyant faculty, though the cards are face downwards, I shall pick out one corresponding with that number. Let me see” (pretends to calculate, and presently turns up a card representing “five”). “You shifted five cards and I have turned up a five, the exact number.”

The cards moved are not replaced, but the performer again retires, and a second person is invited to move a few more from right to left. Again the performer on his return takes up the correct card indicating the number shifted. The trick, unlike most others, may be repeated without fear of detection.

The principle is arithmetical. To begin with, the cards are arranged, unknown to the spectators, in the following order:

Ten, nine, eight, seven, six, five, four, three, two, one.

Such being the case, it will be found that, however many are shifted from right to left, the first card of the new row will indicate their number. Thus, suppose three are shifted. The new order of the cards will then be:

Three, two, one, ten, nine, eight, seven, six, five, four.

So far, the trick is easy enough, but the method of its continuance is a trifle more complicated. To tell the position of the indicating card after the second removal, the performer privately adds the number of that last turned up (in this case three) to its place in the row--one. That gives us four, the card to be turned up after the next shift will be the fourth. Thus, suppose six cards are now shifted, their new order will be:

Nine, eight, seven, six, five, four, three, two, one, ten.

Had five cards only been shifted, the five would have been fourth in the row, and so on.

The performer now adds six, the number of the card, to its place in the row, four: the total, ten, gives him the position of the indicator for the next attempt. Thus, suppose four cards are next shifted, the new order will be:

Three, two, one, ten, nine, eight, seven, six, five, four.

The next calculation, 4 and 10, gives us a total 14. The ten is, in this case, cancelled, and the fourteen regarded as four, which will be found to be the correct indicator for the next shifting.

It looks more mystifying if the performer be blindfolded, for he can tell the position of the cards with his fingers. Keeping his hand on the card, he asks, “Will you please tell me how many cards were shifted?” As soon as the answer is given, he exhibits the card, and can continue the trick as long as he pleases.

5. Find 16 numbers in arithmetical progression (common difference 2) whose sum shall be equal to 7552, and arrange them in 4 columns, 4 numbers in each column--or, in other words, arrange in a square of 16 numbers that when added vertically, horizontally, or diagonally, the sum of each 4 numbers will amount to 1888.

SOME CURIOUS NUMBERS.

If the number 37 be multiplied by 3, or any multiple of 3 up to 27, the product is expressed by three similar digits. Thus--

37 × 3 = 111 37 × 6 = 222 37 × 9 = 333

The products succeed each other in the order of the digits read downwards, 1, 2, 3, etc., these being multiplied by 3 (their number of places) reproduce the multiplicand of 37.