Proven Sudoku
Hidden Unique Rectangle
Also called HUR, Hidden UR.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
The rectangle trick again, but the giveaway is hidden. Instead of spare digits in a corner, you use the fact that a digit has only two homes in a row or column. The rest of the reasoning is the same.
The exact rule, for stronger players
The rule, stated exactly: A rectangle where the uniqueness argument is combined with conjugate-pair links on x or y rather than with naked extras, forcing an elimination in one of the corner cells.
What it removes: Remove the forced digit from the identified corner.
Why it works: Conjugate links constrain which corners can hold x or y. Combining that with the impossibility of the all-{x,y} arrangement forces a specific corner away from a digit. 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.
Related uniqueness
- Reverse BUGThis one uses the numbers you have already filled in, not the ones still open.
- Unique LoopLike a rectangle but longer, a ring of squares all sharing two numbers.
- Unique RectangleFour squares in a rectangle across two boxes, all holding the same two numbers.
- Unique Rectangle Type 1Three corners of the rectangle hold only the two numbers.
- Unique Rectangle Type 2Two corners hold only the pair.
How often does it come up?
Our rough estimate: uncommon, and easily confused with UR Type 4.