21.--A DEAL IN APPLES.
I paid a man a shilling for some apples, but they were so small that I
made him throw in two extra apples. I find that made them cost just a
penny a dozen less than the first price he asked. How many apples did I
get for my shilling?
22.--A DEAL IN EGGS.
A man went recently into a dairyman's shop to buy eggs. He wanted them
of various qualities. The salesman had new-laid eggs at the high price
of fivepence each, fresh eggs at one penny each, eggs at a halfpenny
each, and eggs for electioneering purposes at a greatly reduced figure,
but as there was no election on at the time the buyer had no use for the
last. However, he bought some of each of the three other kinds and
obtained exactly one hundred eggs for eight and fourpence. Now, as he
brought away exactly the same number of eggs of two of the three
qualities, it is an interesting puzzle to determine just how many he
bought at each price.
23.--THE CHRISTMAS-BOXES.
Some years ago a man told me he had spent one hundred English silvercoins in 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 onlya 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 all circles are similar, the same answer will
necessarily apply to any coin. The next question is a most interesting
one to ask a company, each person writing down his answer on a slip of
paper, so that no one shall be helped by the answers of others. What is
the greatest number of three-penny-pieces that may be laid flat on the
surface of a half-crown, so that no piece lies on another or overlaps
the surface of the half-crown? It is amazing what a variety of different
answers one gets to this question. Very few people will be found to give
the correct number. Of course the answer must be given without looking
at the coins.
29.--THE BROKEN COINS.
A man had three coins--a sovereign, a shilling, and a penny--and he
found that exactly the same fraction of each coin had been broken away.
Now, assuming that the original intrinsic value of these coins was the
same as their nominal value--that is, that the sovereign was worth a
pound, the shilling worth a shilling, and the penny worth a penny--what
proportion of each coin has been lost if the value of the three
remaining fragments is exactly one pound?
30.--TWO QUESTIONS IN PROBABILITIES.
There is perhaps no class of puzzle over which people so frequently
blunder as that which involves what is called the theory of
probabilities. I will give two simple examples of the sort of puzzle I
mean. They are really quite easy, and yet many persons are tripped up by
them. A friend recently produced five pennies and said to me: "In
throwing these five pennies at the same time, what are the chances that
at least four of the coins will turn up either all heads or all tails?"
His own solution was quite wrong, but the correct answer ought not to be
hard to discover. Another person got a wrong answer to the following
little puzzle which I heard him propound: "A man placed three sovereigns
and one shilling in a bag. How much should be paid for permission to
draw one coin from it?" It is, of course, understood that you are as
likely to draw any one of the four coins as another.
