The Unique Rectangle in Sudoku
The Unique Rectangle is a clever technique that uses a fact about the puzzle itself. Because a proper Sudoku has exactly one solution, a pattern that would allow two solutions can never complete — and avoiding that “deadly pattern” forces an elimination.
How to use a Unique Rectangle, step by step
- Look for four cells forming a rectangle that sit across exactly two boxes.
- Check whether the same two candidates {X, Y} appear in all four corners.
- If three corners are bi-value {X, Y} and the fourth has {X, Y} plus extras, that fourth cell is the key.
- The puzzle cannot allow the all-{X, Y} version (it would give two solutions), so the fourth cell must take one of its extra digits.
- Eliminate X and Y from that fourth cell, leaving only the extras.
What is the “deadly pattern”?
If four cells forming a rectangle across two boxes all held only the same two candidates {X, Y}, the puzzle would have two valid solutions — you could swap X and Y around the rectangle freely. A properly made Sudoku never allows that, so whenever you are one cell away from it, that cell must break the pattern. This is the only common technique that relies on the puzzle having a unique solution.
How to use it safely
Use Unique Rectangles only on puzzles you trust to be proper (single-solution), such as the boards here. Find a rectangle in two boxes where three corners are exactly {X, Y} and one corner is {X, Y, …}; the extra digits must win, so erase X and Y from that corner. It pairs naturally with naked and hidden pairs. See more in tips & strategy.
Unique Rectangle in Sudoku: FAQ
What is a Unique Rectangle in Sudoku?
A Unique Rectangle is a technique that uses the single-solution guarantee of a proper Sudoku. If four cells in a rectangle across two boxes nearly all share the same two candidates, the pattern that would create two solutions is impossible, which forces a candidate elimination.
Does the Unique Rectangle always work?
Only on properly made puzzles that are guaranteed to have exactly one solution. On a hand-made or faulty puzzle it can give wrong eliminations, so use it only with trusted, single-solution boards.
When should you use a Unique Rectangle?
On Hard, Expert and Evil grids once pairs and singles stall. It is a neat shortcut, but always optional — a logical solve never strictly requires it.