Competition problem — Combinatorics

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Combinatorics Difficulty 4.8 AIME Prove it Belarus

A rectangle $R$ with odd integer side lengths is divided into small rectangles with integer side lengths.
Prove that there is at least one rectangle among the small rectangles whose distances from the four sides of $R$ are either all odd or all even.

Solution

1. See IMO-2017 Shortlist, Problem C1.

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