MathDB

Let

n

be a positive integer, and let M\equal{}\left\{ 1,2,...,n\right\}. Two players take turns at the following game: Each player, at his turn, has to select an element of

M

and remove all divisors of this element (including this element itself) from the set

M

. a) Assume that the player who cannot move anymore (because the set

M

is empty when it's his move) wins. For which values of

n

does the first player have a winning strategy? b) Assume that the player who cannot move anymore (because the set

M

is empty when it's his move) loses. For which values of

n

does the first player have a winning strategy?

Problem Statement