Gurth's Theorem

Gurth's Theorem exploits diagonal or rotational symmetry in Sudoku puzzles to make eliminations. When a puzzle has inherent symmetry, certain candidates can be eliminated based on symmetry constraints.

Pattern Recognition

To apply Gurth's Theorem:

1. Identify if the puzzle has diagonal symmetry (main or anti-diagonal)
2. Or identify if it has 180° rotational symmetry
3. Find cells on the axis of symmetry
4. Apply symmetry constraints to eliminate candidates

How It Works

In a puzzle with diagonal symmetry, cells on the diagonal must either:

• Contain digits that map to themselves under the symmetry, or
• The digit placement must respect the symmetry mapping

This creates constraints that can eliminate candidates.

Example

Documentation stub - examples coming soon.

Related Techniques

• BUG — Another uniqueness-based technique