{"ID":6023322,"CreatedAt":"2026-07-08T01:00:23.257252134Z","UpdatedAt":"2026-07-10T01:11:38.759438437Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.05728","arxiv_id":"2607.05728","title":"Sudoku Grids That Require Many Clues","abstract":"Motivated by worst-case algorithmic time bounds for solving sudoku, we prove that a majority of filled-in $n^2\\times n^2$ sudoku grids require all but a logarithmic fraction of cells to be filled by clues. For $9\\times 9$ and $16\\times 16$ sudoku, we construct grids that require $18$ clues and $80$ clues.","short_abstract":"Motivated by worst-case algorithmic time bounds for solving sudoku, we prove that a majority of filled-in $n^2\\times n^2$ sudoku grids require all but a logarithmic fraction of cells to be filled by clues. For $9\\times 9$ and $16\\times 16$ sudoku, we construct grids that require $18$ clues and $80$ clues.","url_abs":"https://arxiv.org/abs/2607.05728","url_pdf":"https://arxiv.org/pdf/2607.05728v1","authors":"[\"David Eppstein\",\"Xinyu\",\"Zhang\"]","published":"2026-07-07T01:24:40Z","proceeding":"cs.DM","tasks":"[\"cs.DM\",\"cs.DS\"]","methods":"[]","has_code":false}