The Maximum Number of Appearances of a Word in a Grid
Abstract
How can you fill a 3× 3 grid with the letters A and M so that the word ``AMM'' appears as many times as possible in the grid? More generally, given a word w of length n, how can you fill an n× n grid so that w appears as many times as possible? We solve this problem exactly for several families of words, and we asymptotically solve this problem in higher-dimensional grids.
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