September 12, 2010



In the ancient Chinese book Chiu-chang Suan-shu (Nine Chapters on Arithmetic, 九章算术), estimated to have been written some time around 200 B.C., there appears a problem:

A bunch of roosters and rabbits are prisoned in the same cage. One counts from the top, and sees thirty-five heads. One counts from the bottom, and sees ninety-four feet. How many roosters and rabbits are there?

A solution by Sun Zi is as follows:

Suppose one chops off half of the feet for each rooster and rabbits, and is left with forty-seven feet, which accounts for one foot each rooster, and two feet each rabbit. If all the thirty-five heads belong to roosters, then there are supposed to be thirty-five feet. However, for each rabbit, the count for feet increase by one. Since there are twelve more feet in the actual count than thirty-five, the number of rabbits is twelve. There are twenty-three roosters.


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