Question 109
Some cells of a $60 \times 60$ grid is colored black and the rest are colored white. Two players $A$ and $B$ take turns making the following type of move starting from player $A$: choose a black cell and flip the colors of the rectangle that starts on the top-left corner of the grid and ends on the chosen black cell as the bottom-right corner. A player that is not able to make a move - there is no black cell on their turn to move - loses. Find all colorings such that the player $B$ can win regardless of how player $A$ plays.
(Nyamdavaa Amar)
(Nyamdavaa Amar)