100.
“I can divide my sheep,” says Farmer Hodge, who from his schooldays had a turn for figures, “into two unequal parts, so that the larger part added to the square of the smaller part shall be equal to the smaller part added to the square of the larger part.”
How many sheep had the farmer?
A HELPFUL BURDEN
101. The following question was proposed in an old book of Mathematical Curiosities published more than a hundred years ago:—
“It often happens that if we take two horses, in every respect alike, yet, if both are put to the draught, that horse which is most loaded shall be capable of performing most work; so that the horse which carries the heavier weight can draw the larger load. How is this?”
102.
In the king’s treasury were six chests. Two held sovereigns, two shillings, and two pence, in equal numbers of these coins. “Pay my guard,” said the king, “giving an equal share to each man, and three shares to the captain; give change if necessary.” “It may not be possible,” replied the treasurer, “and the captain may claim four shares.” “Tut, tut,” said the king, “it can be done whatever the amount of the treasure, and whether the captain has three shares or four.”