MathDB

There are

2016

positions marked around a circle, with a token on one of them. A legitimate move is to move the token either 1 position or 4 positions from its location, clockwise. The restriction is that the token can not occupy the same position more than once. Players

A

and

B

take turns making moves. Player

A

has the first move. The first player who cannot make a legitimate move loses. Determine which of the two players has a winning strategy.

Problem Statement