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Combinatorics 6.0/10

Dominoes and L-Trominoes

You may use any number of 1 × 2 dominoes (horizontal or vertical) and any number of L-trominoes (three cells forming a 2 × 2 square with one cell missing, in any of its four orientations). In how many ways can a 2 × 8 rectangle be tiled exactly by these pieces? Give an integer.

Related problems & prerequisites

Worth solving first

Source: Classic exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.