Unique Rectangle sudoku technique

Every published sudoku has exactly one solution, and the unique rectangle turns that promise into deductions. Four cells forming a rectangle across exactly two boxes, all containing the same two candidates, would be fatal: the two digits could swap around the rectangle and produce a second valid solution. A proper puzzle cannot allow it, so something must break the pattern — and whatever prevents it is forced.

How to find a unique rectangle

1. Spot a rectangle of four cells spanning two boxes where the same two candidates dominate.
2. If three corners hold only the pair and the fourth carries extras, the fourth cannot collapse to the pair — its extra candidates are where the truth lives.
3. Remove the pair digits from that fourth corner accordingly.
4. Confirm the rectangle sits in exactly two boxes; spread over four boxes, the argument fails.

The pattern on the grid

Worked example

The rectangle r2c2, r2c8, r3c2, r3c8 spans exactly two boxes, and three corners hold the bare pair 7-8. If r3c8 ever collapsed to that pair too, the four corners could swap values and the puzzle would have two solutions — impossible in a verified-unique grid. So r3c8<>78, leaving its extra candidates as the only truth.

When it fails

Verify the four corners span exactly two boxes and that the bare-pair corners truly contain nothing else. A stray extra candidate in a 'clean' corner voids the whole argument — and never use this on puzzles that are not guaranteed unique.

Puzzles that need it

These grids come from rated games on this site — our solver confirmed that unique rectangle was part of the shortest solving path for each one.

Every string is the standard 81-character format (0 = empty) — paste it into any solver to verify the rating and the solving path yourself. Want to try one under the clock? Play a free puzzle — no account needed — or create an account to train specific difficulty tiers.

Related techniques

• X-Wing
• XY-Wing
• Nishio

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