Proven Sudoku
Unique Rectangle Type 1
Also called UR Type 1, UR1.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
Three corners of the rectangle hold only the two numbers. The fourth holds something extra. That fourth corner cannot be either of the two, or the swap would work. So it is one of its extras.
The exact rule, for stronger players
The rule, stated exactly: Three of the four rectangle cells hold exactly {x,y}; the fourth holds {x,y} plus extra candidates. Then x and y are eliminated from the fourth cell.
What it removes: Remove x and y from the cell with extras.
Why it works: If the fourth cell took x or y, all four cells would hold only x and y, completing the deadly pattern. 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 RectangleFour squares in a rectangle across two boxes, all holding the same two numbers.
Related uniqueness
- Unique Rectangle Type 2Two corners hold only the pair.
- 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.
How often does it come up?
Our rough estimate: the most common UR type and usually the easiest to spot.