Question 30
Two players have a pile of identical tokens, from which they alternately take one token each and place it on any empty cell of a square board of size $2008 \times 2008$. The winner is the player who first places a token so that, together with three other tokens, it forms the vertices of an isosceles trapezoid that is not a rectangle and whose bases are parallel to one of the edges of the board. Which player has a winning strategy: the one who started the game, or the other player?