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PreprintCC BY-NC-SA 4.0arXiv

Maximizing Crossword Grids with a Fixed Minimum Clue Length

  • Kelly Isham
  • Abigail Schnitzer
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Abstract

In an American-style crossword puzzle, the grid must be connected, 180-degree symmetric, and have minimum word length 3. Ferland and Pratt construct n× n crossword grids with many clues satisfying these conditions and prove their construction is maximal when n≡ 1 or 3 pmod4. In this paper, we explore American-style crosswords in which the minimum word length is 4. Jacobs computed the maximal 15 × 15 grid with minimum word length 4. In this paper, we construct grids with a maximal number of clues for all n not ≡ 0 pmod5.

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Cite

BibTeXRIS
BibTeX
@misc{isham2026maximizing,
  title = {{Maximizing Crossword Grids with a Fixed Minimum Clue Length}},
  author = {Kelly Isham and Abigail Schnitzer},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03364},
  eprint = {2611.03364},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03364},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Maximizing Crossword Grids with a Fixed Minimum Clue Length
AU  - Kelly Isham
AU  - Abigail Schnitzer
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03364
UR  - https://arxiv.org/abs/2611.03364
AB  - In an American-style crossword puzzle, the grid must be connected, 180-degree symmetric, and have minimum word length 3. Ferland and Pratt construct n× n crossword grids with many clues satisfying these conditions and prove their construction is maximal when n≡ 1 or 3 pmod4. In this paper, we explore American-style crosswords in which the minimum word length is 4. Jacobs computed the maximal 15 × 15 grid with minimum word length 4. In this paper, we construct grids with a maximal number of clues for all n not ≡ 0 pmod5.
ER  -