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IMO 2004 — Complete Shortlist Question 14

IMO Shortlist · IMO 2004 — Complete Shortlist

Question 14

Determine all $ m \times n $ rectangles that can be covered with hooks made up of 6 unit squares, as in the figure:

Question illustration

Rotations and reflections of hooks are allowed. The rectangle must be covered without gaps and overlaps. No part of a hook may cover area outside the rectangle.