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Topic: Is there a formula for the Josephus' problem?
Replies: 0

 John Collins Posts: 2 Registered: 12/10/04
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, Mamako-date San (Scheme for the Benefit of
the Step-children): 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