GridWits
Expert tier Technique 16 of 46 Reference only

Gurth's Theorem

On a puzzle built with 180°-rotational symmetry, the digit that would land on a cell's mirror-image partner must be its complement — narrowing candidates without touching any other unit.

The solver does not attempt this technique, so Smart Hint will never suggest it. It is documented because you may still want to spot it yourself.

How it works

  1. 1This puzzle's given digits are symmetric under 180° rotation, and its complement mapping (worked out from a few solved pairs) sends 7 ↔ 1.
  2. 2A1's mirror partner, I9, is already solved as 7 — so under the complement mapping, A1 must be 1. Its other candidates, 2 and 3, can be eliminated.
  3. 3Only applies to puzzles actually built with that symmetry; GridWits' generator doesn't guarantee it, so this is reference-only here.

Play a Sudoku that needs this technique →

A 1 B 2 C 3 D 4 E 5 F 6 G 7 H 8 I 9 1 2 3 7 2 3
  • Where the conclusion lands
  • Candidate ruled out
Next in the ladder Rectangle Elimination →

A near-Unique-Rectangle pattern where a strong link on one corner forces a contradiction if a second corner (the "wing") holds the shared digit — eliminating it there.