Proven Sudoku
Techniques / Brute force and theory
Unavoidable Sets and Puzzle Generation
Also called Unavoidable set, UA set, Generation theory.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
An unavoidable set is a group of squares you could rearrange to get a second answer. Every valid puzzle needs at least one clue in each such set. Puzzle makers use this to know which clues they cannot remove.
The exact rule, for stronger players
The rule, stated exactly: An unavoidable set is a set of cells in a completed grid that can be permuted into another valid completion. Every uniquely solvable puzzle must contain at least one given inside every unavoidable set.
What it removes: None. This is generation theory, and it is the reason the deadly patterns in Tier 6 exist at all.
Why it works: If a puzzle had no given inside some unavoidable set, both arrangements of that set would extend to full solutions, so the puzzle would not be unique.
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
- Deadly PatternA shape that would give the puzzle two answers if it ever appeared.
- Exact Cover and Dancing LinksA sudoku can be rewritten as a tidy tick box puzzle.
Related brute force
- Difficulty Rating EnginesPrograms give a puzzle a score.
- Minimal Puzzles and the 17-Clue ResultA puzzle is minimal when you cannot take away any clue without giving it a second answer.
- SAT and Constraint Programming EncodingsThe puzzle is turned into a long list of yes or no questions.
How often does it come up?
Our rough estimate: not a solving technique. It is the theory that connects Tier 6 to how puzzles are constructed in the first place.