IMO Shortlist 2006 problem C6


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2. travnja 2012.
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A holey triangle is an upward equilateral triangle of side length n with n upward unit triangular holes cut out. A diamond is a 60^\circ-120^\circ unit rhombus.
Prove that a holey triangle T can be tiled with diamonds if and only if the following condition holds: Every upward equilateral triangle of side length k in T contains at most k holes, for 1\leq k\leq n.
Izvor: Međunarodna matematička olimpijada, shortlist 2006