IMO Shortlist 2006 C6

For discussing Olympiad Level Combinatorics problems
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Phlembac Adib Hasan
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IMO Shortlist 2006 C6

Unread post by Phlembac Adib Hasan » Thu Dec 11, 2014 12:29 pm

A $\small\textit{holey}$ 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 $1\leq k\leq n$.
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