Amusements in Mathematics | Page 8

is not now current.
33.--PUZZLE IN REVERSALS.
Most people know that if you take any sum of money in pounds, shillings, and pence, in
which the number of pounds (less than £12) exceeds that of the pence, reverse it (calling
the pounds pence and the pence pounds), find the difference, then reverse and add this
difference, the result is always £12, 18s. 11d. But if we omit the condition, "less than
£12," and allow nought to represent shillings or pence--(1) What is the lowest amount to
which the rule will not apply? (2) What is the highest amount to which it will apply? Of
course, when reversing such a sum as £14, 15s. 3d. it may be written £3, 16s. 2d., which
is the same as £3, 15s. 14d.
34.--THE GROCER AND DRAPER.
A country "grocer and draper" had two rival assistants, who prided themselves on their
rapidity in serving customers. The young man on the grocery side could weigh up two
one-pound parcels of sugar per minute, while the drapery assistant could cut three
one-yard lengths of cloth in the same time. Their employer, one slack day, set them a race,
giving the grocer a barrel of sugar and telling him to weigh up forty-eight one-pound
parcels of sugar While the draper divided a roll of forty-eight yards of cloth into yard
pieces. The two men were interrupted together by customers for nine minutes, but the
draper was disturbed seventeen times as long as the grocer. What was the result of the
race?
35.--JUDKINS'S CATTLE.
Hiram B. Judkins, a cattle-dealer of Texas, had five droves of animals, consisting of oxen,
pigs, and sheep, with the same number of animals in each drove. One morning he sold all
that he had to eight dealers. Each dealer bought the same number of animals, paying
seventeen dollars for each ox, four dollars for each pig, and two dollars for each sheep;
and Hiram received in all three hundred and one dollars. What is the greatest number of

animals he could have had? And how many would there be of each kind?
36.--BUYING APPLES.
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?
37.--BUYING CHESTNUTS.
Though the following little puzzle deals with the purchase of chestnuts, it is not itself of
the "chestnut" type. It is quite new. At first sight it has certainly the appearance of being
of