MathDB

Let

n

and

k

be given integers such that

n\ge k\ge 2

. Alice and Bob play a game on an

n

n

table with white cells. They take turns to pick a white cell and color it black. Alice moves first. The game ends as soon as there is at least one black cell in every

k

k

square after a player moves, who is declared the winner of the game. Who has the winning strategy?

Problem Statement