Packing Latin squares into sudoku puzzles

I have another new preprint, the result of a research project with UC Irvine undergraduate Cindy Zhang: “Sudoku grids that require many clues” (arXiv:2607.05728, to appear at JCDCG3 2026). The main result is, I think, surprising: When generalized to \(n^2\times n^2\) grids, almost all sudoku puzzles must be almost entirely covered by clues, leaving only a logarithmic fraction of cells blank. This implies an average case time for solving randomly chosen puzzles that is exponential in \(n^4/\log n\), significantly better than the exponential in \(n^4\) that one gets for formulating the problem as an exact cover problem without using this bound on blank cells or the exponential in \(n^4\log n\) that one gets for a brute force search. The formatting requirements for JCDCG3 are in one way quite free-form and in another way very strict: each submission can have only two a4 pages, and the font must be at least 10pt in size, but otherwise you can do what you want. I took advantage of this…