Uniqueness

Uniqueness techniques use the assumption that a published Sudoku has exactly one solution. They prevent patterns that would otherwise allow two digits to be exchanged without violating Sudoku rules.

When to look for it

Look for Uniqueness patterns when four cells form a rectangle across exactly two rows, two columns, and two blocks, and the same two base candidates appear in the rectangle.

Implemented in Xodoku

• Unique Rectangle Type 1 removes the extra candidate that would leave a deadly rectangle.
• Unique Rectangle Type 2 uses a shared extra candidate to remove that digit from peers.
• Unique Rectangle Type 3 combines the rectangle with a subset outside it.
• Unique Rectangle Type 4 uses strong-link style pressure on one base digit.
• Unique Rectangle Type 5 and Type 6 cover additional rectangle placements supported by the solver.
• Hidden Rectangle applies the same logic when extra candidates hide part of the rectangle.
• Avoidable Rectangle Type 1 / 2 use non-given placed digits. They are valid only when the involved digits were entered by the player, not original givens.
• BUG+1 handles a Binary Universal Grave with one extra candidate.

Scope

Xodoku assumes uniqueness techniques are enabled and the puzzle has one solution. If you want to solve without uniqueness assumptions, skip these hints.