Combinatorics · Polyomino tiling · Weighting argument · Invariants · Modular arithmetic · Multiplicative order
For which positive integers \(m\) and \(n\) can an \(m \times n\) rectangle be covered completely and without overlaps by copies of the three figures shown below, each of them built from unit squares? The figures may be moved around, but they may not be rotated or turned over.
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Serbian National Competition (Drzavno takmicenje) 2011, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source