Proven Sudoku
Unique Rectangle Type 2
Also called UR Type 2, UR2.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
Two corners hold only the pair. The other two also hold one extra number, the same one. One of those two must be that extra number. So any square that sees both of them loses it.
The exact rule, for stronger players
The rule, stated exactly: Two cells hold exactly {x,y} and the other two hold {x,y,z} with the same extra digit z. Then z is eliminated from cells seeing both z-bearing cells.
What it removes: Remove z from cells seeing both cells that carry it.
Why it works: At least one of the two cells with extras must be z, otherwise the rectangle completes. So z is present in that pair, excluding it from anything seeing both. This technique is only valid when the puzzle is known to have exactly one solution. It is not a deduction about Sudoku rules, it is a deduction about the puzzle setter's promise. On a grid with multiple solutions it produces wrong answers.
Worked examples
None yet. This pattern does not turn up in our daily boards, so there is no real example to show. We would rather wait than draw a fake one.
Learn these first
- Unique Rectangle Type 1Three corners of the rectangle hold only the two numbers.
Related uniqueness
- Unique Rectangle Type 3Two corners hold the pair.
- Unique Rectangle Type 4Two corners hold only the pair.
- Unique Rectangle Type 5Like Type 2, but the extra number sits in corners that sit across from each other rather than side by side.
- Unique Rectangle Type 6Like Type 4, but the two numbers form an X across the rectangle instead of sitting along one side.
- Unique Rectangle with Missing CandidatesA rectangle where one corner has already lost one of the two numbers.
How often does it come up?
Our rough estimate: common.