Unique Rectangle
Unique Rectangle Type 1
Avoid the pattern that would give a puzzle two solutions: the fourth corner cannot be left with only {x, y}.
Rule
3 corners of a rectangle (2 rows, 2 columns, 2 boxes) hold only {x, y} → remove x and y from the fourth corner.
A rectangle across two boxes
The four cells r6c5, r6c6, r7c5 and r7c6 form a rectangle spanning exactly 2 rows, 2 columns and 2 boxes. Three of them have only the two candidates 2 and 8.
The idea
Take four cells at the corners of a rectangle spanning exactly two rows, two columns and two boxes. If all four held only {x, y}, you could swap x ↔ y in those cells and every row, column and box would still be valid — the puzzle would have two solutions. This is called a deadly pattern.
A proper Sudoku always has exactly one solution. So if three corners are already down to {x, y}, the fourth must be some other digit: remove x and y from it.
This technique relies on the puzzle having a unique solution. Use it only with puzzles from a trustworthy source.
How to spot it
- Find two cells with the same pair {x, y} in one row, in two different boxes; check whether the matching cells in another row close a rectangle.
Common mistakes
- The four cells must lie in exactly two boxes. Across four boxes, swapping breaks a box, so there is no deadly pattern.
- All four cells must be empty, not given digits.
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Related techniques
References
The examples on this page are generated from random puzzles, not taken from these sources.