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Knights on a Round Table

Source: OMM 2008 4

July 19, 2014
combinatorics unsolvedcombinatorics

Problem Statement

A king decides to reward one of his knights by making a game. He sits the knights at a round table and has them call out 1,2,3,1,2,3,…1,2,3,1,2,3,\dots around the circle (that is, clockwise, and each person says a number). The people who say 22 or 33 immediately lose, and this continues until the last knight is left, the winner.
Numbering the knights initially as 1,2,…,n1,2,\dots,n, find all values of nn such that knight 20082008 is the winner.
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