Proven Sudoku
Techniques / Exotic and rank-zero
Gurth's Symmetrical Placement
Also called GSP, Symmetrical placement, Gurth's theorem.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
Some puzzles are built with a mirror pattern. If the clues are symmetric and the digits match that symmetry, the answer must be symmetric too. That lets you fill in partners without solving them one at a time.
The exact rule, for stronger players
The rule, stated exactly: If a puzzle's givens are invariant under a symmetry that maps digits to digits, then in a uniquely solvable puzzle the solution must share that symmetry, which forces placements along the symmetry's fixed points.
What it removes: Force the symmetric relationships, typically placing digits on the diagonal and pairing digits elsewhere.
Why it works: Applying the symmetry to a solution yields another solution. Uniqueness forces the two to be identical, so the solution is symmetric. This depends entirely on the puzzle having exactly one solution and is invalid otherwise.
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.
Related exotic and rank-zero
- Homogeneous ChainsA chain where every link is the same kind.
- Junior ExocetTwo squares act as a launcher and two more as the target.
- Multi-Sector Locked SetsCount several rows, columns and boxes at once.
- Pattern Overlay MethodEvery digit has to land in one of a fixed set of shapes across the grid.
- Rank TheoryA way to count a pattern.
How often does it come up?
Our rough estimate: rare, and only applicable to deliberately symmetric puzzles.