Question 2
Let $a,b$ be positive integers. Every cell of an $(a+b+1)\times(a+b+1)$ grid is amber or bronze, with at least $a^2+ab-b$ amber and at least $b^2+ab-a$ bronze cells. Prove that one can choose $a$ amber and $b$ bronze cells, no two in the same row or column.
Proposed by Ankan Bhattacharya. Source: Evan Chen’s third-party solution notes; https://aops.com/community/p24774812. One point is a nonofficial editorial normalization; this essay requires manual grading.
Proposed by Ankan Bhattacharya. Source: Evan Chen’s third-party solution notes; https://aops.com/community/p24774812. One point is a nonofficial editorial normalization; this essay requires manual grading.