Avoidable Rectangle

Also called AR, Avoidable Rectangle (general).

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

Four squares can form a rectangle across two boxes. If three of them were worked out rather than printed, and the fourth would complete a swappable set, the puzzle would have two answers. Since it has one, that fourth digit is wrong.

The exact rule, for stronger players

The rule, stated exactly: A rectangle whose corners include already-placed digits that were not givens. If completing the rectangle with two digits in two boxes would create a deadly pattern, the completing candidate is eliminated.

What it removes: Remove the candidate that would complete the deadly rectangle.

Why it works: Placed digits that are not givens are themselves deductions. If a rectangle of solved non-given cells plus one unsolved cell could permute, the puzzle would not be unique, so the permuting arrangement is impossible. 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

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.
BUG+1Say every open square had two numbers left, and each number had two homes in every group.

How often does it come up?

Our rough estimate: uncommon, and dependent on which cells were givens, which makes it the uniqueness technique most often applied incorrectly.

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