Combinatorics · Polyomino tiling · Area counting · Divisibility bound · Explicit construction · Extremal problem
Find the smallest natural number \(n\) for which an \(n \times n\) board of unit cells can be covered completely and without overlaps by equally many tiles of the two shapes below: an \(L\)-shaped tile of four cells (a row of three with one further cell attached above its left end) and a \(U\)-shaped tile of five cells (a row of three with one further cell attached above each end).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2007, 1. letnik, category A, problem 4. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source