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Making an 11x11 hole in a 2011x2011 board tiled with dominos

Source: XVIII Tuymaada Mathematical Olympiad (2011), Junior Level

July 29, 2011
geometryrectanglecombinatorics

Problem Statement

How many ways are there to remove an 11×1111\times11 square from a 2011×20112011\times2011 square so that the remaining part can be tiled with dominoes (1×21\times 2 rectangles)?
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