Proven Sudoku
Techniques / Brute force and theory
Minimal Puzzles and the 17-Clue Result
Also called 17 clue sudoku, Minimum number of givens, Minimal puzzle.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
A puzzle is minimal when you cannot take away any clue without giving it a second answer. People wondered for years how few clues a sudoku can have. The answer is 17. A huge computer search proved no 16 clue puzzle works.
The exact rule, for stronger players
The rule, stated exactly: A puzzle is minimal if removing any given destroys uniqueness. An exhaustive computational search established that no uniquely solvable 9x9 Sudoku exists with 16 givens, making 17 the minimum.
What it removes: None.
Why it works: The 17-clue result is a computational proof by exhaustive search over equivalence classes, not a hand argument. It is cited, not reproduced.
Worked examples
None yet. This pattern does not turn up in our daily boards, so there is no real example to show. We would rather wait than draw a fake one.
Learn these first
- Exact Cover and Dancing LinksA sudoku can be rewritten as a tidy tick box puzzle.
- Deadly PatternA shape that would give the puzzle two answers if it ever appeared.
Related brute force
- SAT and Constraint Programming EncodingsThe puzzle is turned into a long list of yes or no questions.
- Unavoidable Sets and Puzzle GenerationAn unavoidable set is a group of squares you could rearrange to get a second answer.
- Difficulty Rating EnginesPrograms give a puzzle a score.
How often does it come up?
Our rough estimate: not a technique. Included because it is the most commonly searched Sudoku fact and connects directly to unavoidable sets.