Part 38

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.

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.”