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Combinatorics 6.0/10

Dominoes on a 3 × 10 Board

In how many ways can a 3 × 10 rectangle be tiled completely by fifteen 1 × 2 dominoes (each placed horizontally or vertically)? Tilings related by a symmetry of the rectangle count as different. Give an integer.

Related problems & prerequisites

Worth solving first

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