Proven Sudoku
Unique Loop
Also called UL, Uniqueness Loop, Bivalue loop.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
Like a rectangle but longer, a ring of squares all sharing two numbers. If the ring held only those two, it could be flipped for a second answer. So the ring must be broken somewhere.
The exact rule, for stronger players
The rule, stated exactly: A closed loop of cells, even in length, alternating between two houses of each type, all holding the same two candidates. The loop is a deadly pattern of the same kind as the rectangle, generalized beyond four cells.
What it removes: Follows the UR type structure: extras in one cell lose the loop digits, common extras license external eliminations, and so on.
Why it works: An even loop confined to two digits admits two alternating assignments, both valid, so a unique puzzle cannot permit one to be free. 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 1Three corners of the rectangle hold only the two numbers.
- 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.
How often does it come up?
Our rough estimate: uncommon. The rectangle is the length-four case.