Sudoku Grids That Require Many Clues

David Eppstein; Xinyu; Zhang

Sudoku Grids That Require Many Clues

Discrete Mathematics 2026-07-07 v1 Data Structures and Algorithms

Authors: David Eppstein , Xinyu , Zhang

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.

Cite

@article{arxiv.2607.05728,
  title  = {Sudoku Grids That Require Many Clues},
  author = {David Eppstein and Xinyu and Zhang},
  journal= {arXiv preprint arXiv:2607.05728},
  year   = {2026}
}

Comments

2 pages; to appear at 28th Japan Conference on Discrete and Computational Geometry, Graphs, and Games, Tokyo, 2026