Unique Rectangle (Type 1) is a "uniqueness" strategy. Unlike other strategies that use pure logic to find what must be true, this strategy uses the rules of Sudoku design to find what cannot be true.
The Golden Rule: A valid Sudoku puzzle must have exactly one unique solution.
If a pattern exists that would allow for two valid solutions, we know that pattern is impossible.
Interactive Example
Click "Apply Logic" to see the strategy in action.
The "Deadly Pattern"
Imagine four cells forming a rectangle (2 rows, 2 columns, within 2 boxes) that all contain the exact same pair, like {1, 2}.
- R1C7: {1, 2}
- R1C8: {1, 2}
- R4C7: {1, 2}
- R4C8: {1, 2}
If this state existed, you could swap the 1s and 2s diagonally and both arrangements would result in a valid Sudoku.
Since a proper Sudoku cannot have two solutions, this state (four identical bivalue cells in a rectangle) is called a Deadly Pattern. We must avoid it.
Real Example Explanation
In the example above:
- Three Floor Cells: Look at R1C7, R1C8, and R4C8. They contain only {1, 2}.
- The Target: Look at the fourth corner, R4C7 (highlighted).
- It contains {1, 2} plus extra candidates.
- The Logic:
- If R4C7 were reduced to just {1, 2}, we would create the Deadly Pattern—four identical bivalue cells forming a rectangle.
- To prevent the Deadly Pattern, R4C7 CANNOT be 1 or 2.
- It must be one of the "extra" candidates.
- The Elimination:
- We remove 1 and 2 from R4C7.
- This leaves only the extra candidates, breaking the deadly pattern.
How to Spot It
- Find a Pair: Look for two bivalue cells in the same row or column (the "Floor").
- Find a Third Corner: Look for another bivalue cell in the rectangle that matches the pair.
- Check the Fourth Corner:
- Does it span exactly two boxes? (e.g. Columns 3 and 9 are in different boxes).
- Does the fourth cell have the pair plus extra candidates?
- Eliminate: Remove the pair candidates from the fourth cell.