Combinatorics · Polyomino tilings · Counting invariant · Corner forcing · Extremal count
An \(8 \times 8\) board is tiled with copies of the three figures below.
The figures may be rotated and reflected, and any number of copies of each of the three shapes may be used; the board counts as tiled when every one of its cells is covered by exactly one figure. Determine the smallest possible number of copies of the first of the three shapes that such a tiling can use.
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Serbian Regional Competition (Okruzno takmicenje) 2022, high school grade I, category A, problem 5. Organized by the Mathematical Society of Serbia (DMS). Source