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Is there a formula for the Josephus' problem?
Posted:
Sep 11, 1996 7:05 PM


The problem is how to arrange 15 Christians and 15 Turks in a circle so that, by throwing every ninth person into a pond, the Turks are eliminated one by one until only all 15 Christians remain.
There is a Japanese variant, Mamakodate San (Scheme for the Benefit of the Stepchildren): how does a stepmother arrange her own 15 children and the 15 stepchildren from her husband's previous marriage so that, by eliminating every tenth child, only her own children survive.
The correct sequence for each can be established by counting it out with 30 bits of paper, but I was wondering if there is a mathematical formula that could be used.
 John Collins



