MathDB

Let

n

be a positive integer. E. Chen and E. Chen play a game on the

n^2

points of an

n \times n

lattice grid. They alternately mark points on the grid such that no player marks a point that is on or inside a non-degenerate triangle formed by three marked points. Each point can be marked only once. The game ends when no player can make a move, and the last player to make a move wins. Determine the number of values of

n

between

1

and

2013

(inclusive) for which the first player can guarantee a win, regardless of the moves that the second player makes.
Ray Li

Problem Statement