Let a and b be positive integers. The cells of an (a+b+1)×(a+b+1) grid are colored amber and bronze such that there are at least a2+ab−b amber cells and at least b2+ab−a bronze cells. Prove that it is possible to choose a amber cells and b bronze cells such that no two of the a+b chosen cells lie in the same row or column. USAMOcombinatoricsgridsUSAMO 2022