On the Minimum Number of Pieces for Two-Dimensional Anti-Slide Using T-Tetrominoes

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<p>Given a box of some specified size and a number of pieces of some specified shape, the anti-slide problem considers how to pack the pieces such that none of the pieces in the box can slide in any direction. The object is to find such a sparsest packing. In this paper, we consider the problem for the case of a two-dimensional square box using T-tetromino pieces. We show that, for a square box of side length n, the number of pieces in a sparsest packing is exactly $\lfloor 2n/3 \rfloor$ when n≢0 (mod 3), and is between 2n/3-1 and n-1 when n≡0 (mod 3).</p>

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