BUYING APPLES.
(
Money Puzzles)
As the purchase of apples in small quantities has always presented
considerable difficulties, I think it well to offer a few remarks on
this subject. We all know the story of the smart boy who, on being told
by the old woman that she was selling her apples at four for threepence,
said: "Let me see! Four for threepence; that's three for twopence, two
for a penny, one for nothing--I'll take _one_!"
There are similar cases of perplexity. For example, a boy once picked up
a penny apple from a stall, but when he learnt that the woman's pears
were the same price he exchanged it, and was about to walk off. "Stop!"
said the woman. "You haven't paid me for the pear!" "No," said the boy,
"of course not. I gave you the apple for it." "But you didn't pay for
the apple!" "Bless the woman! You don't expect me to pay for the apple
and the pear too!" And before the poor creature could get out of the
tangle the boy had disappeared.
Then, again, we have the case of the man who gave a boy sixpence and
promised to repeat the gift as soon as the youngster had made it into
ninepence. Five minutes later the boy returned. "I have made it into
ninepence," he said, at the same time handing his benefactor threepence.
"How do you make that out?" he was asked. "I bought threepennyworth of
apples." "But that does not make it into ninepence!" "I should rather
think it did," was the boy's reply. "The apple woman has threepence,
hasn't she? Very well, I have threepennyworth of apples, and I have just
given you the other threepence. What's that but ninepence?"
I cite these cases just to show that the small boy really stands in need
of a little instruction in the art of buying apples. So I will give a
simple poser dealing with this branch of commerce.
An old woman had apples of three sizes for sale--one a penny, two a
penny, and three a penny. Of course two of the second size and three of
the third size were respectively equal to one apple of the largest size.
Now, a gentleman who had an equal number of boys and girls gave his
children sevenpence to be spent amongst them all on these apples. The
puzzle is to give each child an equal distribution of apples. How was
the sevenpence spent, and how many children were there?
Answer:
As there were the same number of boys as girls, it is clear that the
number of children must be even, and, apart from a careful and exact
reading of the question, there would be three different answers. There
might be two, six, or fourteen children. In the first of these cases
there are ten different ways in which the apples could be bought. But we
were told there was an equal number of "boys and girls," and one boy and
one girl are not boys and girls, so this case has to be excluded. In the
case of fourteen children, the only possible distribution is that each
child receives one halfpenny apple. But we were told that each child was
to receive an equal distribution of "apples," and one apple is not
apples, so this case has also to be excluded. We are therefore driven
back on our third case, which exactly fits in with all the conditions.
Three boys and three girls each receive 1 halfpenny apple and 2
third-penny apples. The value of these 3 apples is one penny and
one-sixth, which multiplied by six makes sevenpence. Consequently, the
correct answer is that there were six children--three girls and three
boys.
