Amusements in Mathematics | Page 6

Christmas-boxes, giving every person the same amount, and it cost him exactly £1, 10s.
1d. Can you tell just how many persons received the present, and how he could have
managed the distribution? That odd penny looks queer, but it is all right.
24.--A SHOPPING PERPLEXITY.
Two ladies went into a shop where, through some curious eccentricity, no change was
given, and made purchases amounting together to less than five shillings. "Do you
know," said one lady, "I find I shall require no fewer than six current coins of the realm
to pay for what I have bought." The other lady considered a moment, and then exclaimed:
"By a peculiar coincidence, I am exactly in the same dilemma." "Then we will pay the
two bills together." But, to their astonishment, they still required six coins. What is the
smallest possible amount of their purchases--both different?
25.--CHINESE MONEY.
The Chinese are a curious people, and have strange inverted ways of doing things. It is
said that they use a saw with an upward pressure instead of a downward one, that they
plane a deal board by pulling the tool toward them instead of pushing it, and that in
building a house they first construct the roof and, having raised that into position, proceed
to work downwards. In money the currency of the country consists of taels of fluctuating
value. The tael became thinner and thinner until 2,000 of them piled together made less
than three inches in height. The common cash consists of brass coins of varying
thicknesses, with a round, square, or triangular hole in the centre, as in our illustration.
[Illustration]
These are strung on wires like buttons. Supposing that eleven coins with round holes are

worth fifteen ching-changs, that eleven with square holes are worth sixteen ching-changs,
and that eleven with triangular holes are worth seventeen ching-changs, how can a
Chinaman give me change for half a crown, using no coins other than the three
mentioned? A ching-chang is worth exactly twopence and four-fifteenths of a
ching-chang.
26.--THE JUNIOR CLERK'S PUZZLE.
Two youths, bearing the pleasant names of Moggs and Snoggs, were employed as junior
clerks by a merchant in Mincing Lane. They were both engaged at the same salary--that
is, commencing at the rate of £50 a year, payable half-yearly. Moggs had a yearly rise of
£10, and Snoggs was offered the same, only he asked, for reasons that do not concern our
puzzle, that he might take his rise at £2, 10s. half-yearly, to which his employer (not,
perhaps, unnaturally!) had no objection.
Now we come to the real point of the puzzle. Moggs put regularly into the Post Office
Savings Bank a certain proportion of his salary, while Snoggs saved twice as great a
proportion of his, and at the end of five years they had together saved £268, 15s. How
much had each saved? The question of interest can be ignored.
27.--GIVING CHANGE.
Every one is familiar with the difficulties that frequently arise over the giving of change,
and how the assistance of a third person with a few coins in his pocket will sometimes
help us to set the matter right. Here is an example. An Englishman went into a shop in
New York and bought goods at a cost of thirty-four cents. The only money he had was a
dollar, a three-cent piece, and a two-cent piece. The tradesman had only a half-dollar and
a quarter-dollar. But another customer happened to be present, and when asked to help
produced two dimes, a five-cent piece, a two-cent piece, and a one-cent piece. How did
the tradesman manage to give change? For the benefit of those readers who are not
familiar with the American coinage, it is only necessary to say that a dollar is a hundred
cents and a dime ten cents. A puzzle of this kind should rarely cause any difficulty if
attacked in a proper manner.
28.--DEFECTIVE OBSERVATION.
Our observation of little things is frequently defective, and our memories very liable to
lapse. A certain judge recently remarked in a case that he had no recollection whatever of
putting the wedding-ring on his wife's finger. Can you correctly answer these questions
without having the coins in sight? On which side of a penny is the date given? Some
people are so unobservant that, although they are handling the coin nearly every day of
their lives, they are at a loss to answer this simple question. If I lay a penny flat on the
table, how many other pennies can I place around it, every one also lying flat on the table,
so that they all touch the first one? The geometrician will, of course, give the answer at
once, and not need to make any experiment. He will also know that, since