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Dividing a Grid into Polygons

Source: Tournament of Towns Fall 2015 Senior A-level

February 23, 2017
combinatoricscombinatorial geometry

Problem Statement

A 10×1010 \times 10 square on a grid is split by 8080 unit grid segments into 2020 polygons of equal area (no one of these segments belongs to the boundary of the square). Prove that all polygons are congruent. (66 points)
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