Unique Rectangle with Missing Candidates

Also called UR with missing candidates, Incomplete UR.

New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.

This technique assumes the puzzle has exactly one solution. It reasons about what would create a second solution, so it is only valid on a properly constructed puzzle. Do not use it to check whether a grid is well formed.

What it means

A rectangle where one corner has already lost one of the two numbers. It cannot make the bad shape any more. That missing number is the clue, and it tells you what the other corners must do.

The exact rule, for stronger players

The rule, stated exactly: A rectangle where one or more of the four cells lacks x or y as a candidate. Some UR types still apply, because the deadly pattern only requires that the arrangement be reachable.

What it removes: Depends on which candidates are missing. The page must enumerate the safe and unsafe cases explicitly.

Why it works: The deadly pattern argument needs the four cells to be able to hold only x and y. A missing candidate can make the pattern unreachable, which invalidates the deduction, or can leave it reachable, which preserves it. Each case must be checked rather than assumed. 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

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.
BUG-LiteThe pattern applied to part of the grid rather than all of it.

How often does it come up?

Our rough estimate: this is where most incorrect UR claims come from, which is why it needs its own page rather than a footnote.

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