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USAJMO 2023 Question 4

USAJMO · USAJMO 2023

Question 4

Blake and Ruby play on an infinite grid, initially white. Starting with Blake, they alternate turns. Blake colors one white square blue; Ruby colors two white squares red. Blake may end the game. His score is the number of unit squares in the largest simple polygon consisting only of blue unit squares. What is the largest score Blake can guarantee?

Proposed by David Torres. Source: Evan Chen’s third-party compilation; https://aops.com/community/p27349414. One editorial point; manual grading.