Unique Rectangle
A pattern that would create two solutions. Since a proper puzzle has only one, it can be ruled out.
What it is
A unique rectangle involves four cells at the corners of a rectangle spanning exactly two rows, two columns and two boxes. If all four held the same two candidates, the two digits could be swapped diagonally and the puzzle would have two solutions. Proper Sudoku has exactly one, so that configuration is impossible — which lets you eliminate candidates from the corner that still carries extras.
How to spot it
Look for three cells with identical pairs at three corners of a rectangle, where the fourth corner contains those two digits plus others. Check that the rectangle covers only two boxes. Then remove the two pair digits from the fourth corner.
Worked example
Step through the reasoning below. Each step adds one layer: first the position, then the pattern, then the candidates involved, and finally what can be eliminated.
Step 1 of 4: The starting position
- Pattern cells
- 7/4, 7/6, 1/4, 1/6
- Digits
- 1, 5
- Eliminations
- 1/4, 1/6
Press a marked square to point it out on the board above.
Why it matters
Uniqueness techniques are the only ones that use a property of the puzzle rather than the grid. They are fast and effective, though purists avoid them because they assume the setter guaranteed a single solution.
Frequently asked questions
Why must the rectangle span exactly two boxes?
Because only then can the two digits be swapped diagonally without breaking any constraint. Spanning four boxes would put each digit in a different box, and the swap would not produce a second valid solution.
Is it fair to use this technique?
It is a matter of taste. It relies on the puzzle being properly constructed rather than on the grid alone. Every puzzle from a reputable source, including ours, has exactly one solution, so the assumption holds.
What if all four corners have exactly the pair?
Then the puzzle has two solutions and is not a proper Sudoku. If you see that, one of your pencil marks is wrong.
Put it to use
Where you will meet it
Expert grids are the only place this pattern regularly decides the solve. Bring your notes.
Play ExpertStuck on a grid of your own?
Type the position into the solver and it walks the whole solution, naming the technique behind every step — including this one.
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