Cats in Cubes

  • Noah Kravitz
  • Noga Alon

Abstract

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 $\mathsf{CAT}$ can appear contiguously at most $(3^{d-1}/2)n^d$ times (allowing diagonals); we also characterize when equality occurs and extend our results to words other than $\mathsf{CAT}$.

Published
2024-09-20
Article Number
P3.29