“A man had a piece of land exactly square, and having four trees scattered over it, as you see in the picture. The house took up one quarter of the land, and was occupied by four tenants. The owner promised them the use of the land, rent free, if they could divide it into four parts of the same size and shape, and each to have one tree. The question is, how did they do it?”
After some little puzzling of wits, the lot was divided as in the annexed illustration, and the tenants were congratulated on the good bargain they had made.
“Otis,” said Ronald, “I’ll bet you can’t tell what the half of nine is.”
“It’s four and a half—any fool might know that,” replied Otis.
“No it isn’t,” continued Ronald, “it’s either four or six, just as you please, and I can prove it;” and writing IX, he folded the paper across the middle and made his promise good.
“Speaking of arithmetical puzzles,” said Aunt Fanny, “I remember one that I worked over for a long time, before I could see into it. It was something like this: Two Arabs sat down to dinner, one having five loaves, and the other three. A stranger came along and asked permission to eat with them, which they granted. After the stranger had dined, he laid down eight pieces of money and departed. The owner of the five loaves took five pieces, and left three for the other, who thought he had not received his share. So they went to a magistrate, and he ordered that the owner of the five loaves should have seven pieces of the money, and the other only one. Was this just?”
“Why, no, it’s plain enough that it wasn’t,” said Otis. “Each man ought to have as many pieces of money as he had loaves.”
“Yes, it was just,” continued Aunt Fanny; “otherwise you would pay the man of three loaves for the bread he ate himself. To prove this, divide each loaf into three equal parts, making in all twenty-four parts, and take it for granted that each person ate an equal or one-third part of the whole. You will find that the stranger had seven parts of the person who contributed five loaves or fifteen parts, and only one of him who contributed three loaves, or nine parts.”
“O yes, I see into it, now,” said Otis.