Amusements in Mathematics
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?
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
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?