Math CentralQuandaries & Queries


Question from Jim, a parent:

An evil Mayan emperor decides to make an example of 1,000 prisoners. He stands them in a circle with numbers one to a thousand marked on their shirts. He then starts counting: "one in, two, in three out" The third man is immediately executed. This continues round and round and round the circle. While the number in the circle shrinks, every third prisoner is pushed out and executed. And it continues even when there are only two prisoners left alive. What number is on the last prisoner's shirt?

Is there a general rule for finding the last man without actually doing the problem mechanically or with a computer. Mechanically can involve you in too many mistakes. With a computer, well they didn't have one at the time of the Mayan civilization.

Is there a general rule if it were, say, every seventh prisoner?

This problem has had me stumped for more than 40 years. Please help!




This is known as the Josephus problem.
For history and a solution outline, see


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