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IMO ShortList 1999, combinatorics problem 2

Source: IMO ShortList 1999, combinatorics problem 2

November 14, 2004
geometryrectanglecombinatoricscountingIMO Shortlist

Problem Statement

If a 5×n5 \times n rectangle can be tiled using nn pieces like those shown in the diagram, prove that nn is even. Show that there are more than 2⋅3k−12 \cdot 3^{k-1} ways to file a fixed 5×2k5 \times 2k rectangle (k≥3)(k \geq 3) with 2k2k pieces. (symmetric constructions are supposed to be different.)
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