MathDB

Let

a

and

b

be positive integers. The cells of an

(a+b+1)\times (a+b+1)

grid are colored amber and bronze such that there are at least

a^2+ab-b

amber cells and at least

b^2+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.

Problem Statement