MathDB

Tiling rectangle with smaller rectangles.

Source: IMO Shortlist 2017 C1

July 10, 2018

rectangleIMO ShortlistcombinatoricsTiling

Problem Statement

A rectangle

\mathcal{R}

with odd integer side lengths is divided into small rectangles with integer side lengths. Prove that there is at least one among the small rectangles whose distances from the four sides of

\mathcal{R}

are either all odd or all even.
Proposed by Jeck Lim, Singapore

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