MathDB

From a square board

1000\times 1000

four rectangles

2\times 994

have been cut off as shown on the picture. Initially, on the marked square there is a centaur - a piece that moves to the adjacent square to the left, up, or diagonally up-right in each move. Two players alternately move the centaur. The one who cannot make a move loses the game. Who has a winning strategy? https://cdn.artofproblemsolving.com/attachments/c/6/f61c186413b642b5b59f3947bc7a108c772d27.png

Problem Statement