Problem #PRU-78535

Problem

Two players play on a square field of size $99\times 99$, which has been split onto cells of size $1\times 1$. The first player places a cross on the center of the field; After this, the second player can place a zero on any of the eight cells surrounding the cross of the first player. After that, the first puts a cross onto any cell of the field next to one of those already occupied, etc. The first player wins if he can put a cross on any corner cell. Prove that with any strategy of the second player the first can always win.