N×N disks are placed on a square game board. Each disk has a black side and white side.
At each turn, you may choose a disk and flip all the disks in the same row and the same column as this disk: thus 2×N-1 disks are flipped. The game ends when all disks show their white side. The following example shows a game on a 5×5 board.
It can be proven that 3 is the minimal number of turns to finish this game.
The bottom left disk on the N×N board has coordinates (0,0);