EGMO 2026 Problem 1
- Day 1
A board is said to be bordeaux if at least one of its unit cells is coloured red. A rectangular region made of cells is oddly-rectangular if it contains an odd number of red cells. Determine the largest positive integer such that, in every possible bordeaux board, there exists an oddly-rectangular region of at least cells.
Note: A rectangular region has sides that are parallel to the sides of the board and contains all of its interior.
Official text European Girls' Mathematical Olympiad 2026 official paper, page 1. Quoted with source.
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