Answering a recent question of Patchell and Spiro, we show that when a d-dimensional cube of side length n is filled with letters, the word CAT can appear contiguously at most (3ᵈ⁻¹/2)nᵈ times (allowing diagonals); we also characterize when equality occurs and extend our results to words other than CAT.
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Kravitz et al. (2024) studied this question.
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