Avoidable Rectangle Type 1

Also called AR Type 1, AR1.

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

Three corners of a rectangle were worked out by you, not printed in the puzzle. If the fourth corner completed the swappable shape, the puzzle would have two answers. So that number is out.

The exact rule, for stronger players

The rule, stated exactly: Three corners are solved non-given cells forming three corners of a potential deadly rectangle. The fourth cell loses the candidate that would complete it.

What it removes: Remove the completing digit from the fourth cell.

Why it works: Completing the rectangle would allow a permutation of the four cells, contradicting uniqueness. 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

Avoidable RectangleFour squares can form a rectangle across two boxes.

Related uniqueness

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.
BUG+2The same idea when two squares break the pattern instead of one.

How often does it come up?

Our rough estimate: the most common AR form.

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