Finding black squares
Source: Iran MO 2nd round 2022 , P4
May 10, 2022
combinatorics
Problem Statement
There is an table with some unit cells colored black and the others are white.
In each step , Amin takes a with exactly one black cell in it , and color all cells in that black cell's red.
While Ali , takes a with exactly one black cell in it , and color all cells in that black cell's red.
Prove that Amin can color all the cells red , iff Ali can do so.