How Sudoku Puzzles Are Generated

A solved Sudoku is a Latin square with an extra box constraint. Generators build one by backtracking: place a legal digit, move to the next cell, and reverse when a cell has no legal option. Randomising the digit order at each step is what makes successive grids different rather than producing the same canonical solution every time.

Clues are removed one at a time, and after each removal the puzzle is re-solved to count solutions. If more than one solution exists, the digit is put back. This is why difficulty correlates loosely with clue count: the process naturally stops when no further digit can be removed, and where it stops depends on which digits were tried in which order.

A puzzle where no further clue can be removed is called minimal. Minimal is not the same as hard.

Counting clues is a poor difficulty measure. The meaningful measure is which techniques a solver must apply — a puzzle needing only naked singles is easy regardless of clue count, and one requiring X-Wing is not. Rating by required technique is why the labels on this site correspond to the same experience across difficulties.

No 9×9 Sudoku with 16 or fewer givens has a unique solution. This was not proved by argument but by exhaustive computer search — Gary McGuire's team checked every essentially different 16-clue configuration in 2012, a computation taking roughly 7.1 million core-hours. The result stands as one of the few hard numerical facts about Sudoku.

Puzzles on this site range from 20 to 45 clues depending on difficulty; see the format reference for exact counts.

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