Sudoku Solving and Finding Magic Squares by Probability Models and Markov Chains
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917443037822976 |
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| author | Hjort, Nils Lid |
| author_facet | Hjort, Nils Lid |
| contents | The sudoku puzzles have a long history, with variations going back more than a hundred years, but its current and perhaps surprising world-wide prominence goes back to certain initiatives and then puzzle-generating computer programmes from just after 2000. To solve a sudoko puzzle, a statistician can put up a probabilitymodel on the enormous space of $9\times9$ matrix possibilities, constructed to favour `good attempts', and then engineer a Markov chain to sample a long enough chain of sudoku table realisations from that model, until the solution is found. The methods work also for other types of puzzles, like constructing `magic squares' with wished-for properties (sums of rows, columns, diagonals equal, etc.), as is also illustrated in this article; via magic models and equally magic Markov chains I find impressively magic $8\times8$ and $10\times10$ squares. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_25402 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sudoku Solving and Finding Magic Squares by Probability Models and Markov Chains Hjort, Nils Lid Other Statistics The sudoku puzzles have a long history, with variations going back more than a hundred years, but its current and perhaps surprising world-wide prominence goes back to certain initiatives and then puzzle-generating computer programmes from just after 2000. To solve a sudoko puzzle, a statistician can put up a probabilitymodel on the enormous space of $9\times9$ matrix possibilities, constructed to favour `good attempts', and then engineer a Markov chain to sample a long enough chain of sudoku table realisations from that model, until the solution is found. The methods work also for other types of puzzles, like constructing `magic squares' with wished-for properties (sums of rows, columns, diagonals equal, etc.), as is also illustrated in this article; via magic models and equally magic Markov chains I find impressively magic $8\times8$ and $10\times10$ squares. |
| title | Sudoku Solving and Finding Magic Squares by Probability Models and Markov Chains |
| topic | Other Statistics |
| url | https://arxiv.org/abs/2604.25402 |