On The Minimum Number Of Pieces For Two-Dimensional Anti-Slide Using T-Tetrominoes

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 [2n/3] when n not equivalent to 0 (mod 3), and is between 2n/3 - 1 and n - 1 when n 0 (mod 3).