Proven Sudoku
Unique Rectangle Type 6
Also called UR Type 6, UR6.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
Like Type 4, but the two numbers form an X across the rectangle instead of sitting along one side. One of the corners is forced, and the other number goes.
The exact rule, for stronger players
The rule, stated exactly: Two diagonally opposite cells hold exactly {x,y}, and digit x is confined to the rectangle in both the rows and the columns involved. Then x is eliminated from the two cells with extras, forcing them to y.
What it removes: Remove x from the two cells with extras.
Why it works: An X-Wing style confinement of x on the rectangle means x occupies one diagonal. If it occupied the diagonal with the bivalue cells, the rectangle would complete, so it takes the other diagonal. 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 4Two corners hold only the pair.
- X-WingA digit is stuck in the same two columns in two different rows, making a rectangle.
Related uniqueness
- Unique Rectangle with Missing CandidatesA rectangle where one corner has already lost one of the two numbers.
- Avoidable RectangleFour squares can form a rectangle across two boxes.
- Avoidable Rectangle Type 1Three corners of a rectangle were worked out by you, not printed in the puzzle.
- Avoidable Rectangle Type 2The same idea, but two corners are still open and share an extra number.
- Bivalue Universal GraveSay every open square had just two numbers left.
How often does it come up?
Our rough estimate: uncommon.