Avoidable Rectangle Type 2

Also called AR Type 2, AR2.

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

The same idea, but two corners are still open and share an extra number. One of them must take that extra. Anything that sees both loses it.

The exact rule, for stronger players

The rule, stated exactly: Two corners solved and two unsolved carrying a common extra digit. That digit must appear in one of them, licensing elimination from cells seeing both.

What it removes: Remove the extra digit from cells seeing both unsolved corners.

Why it works: As for UR Type 2, with solved cells supplying two corners of the pattern. 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 Rectangle Type 1Three corners of a rectangle were worked out by you, not printed in the puzzle.

Related uniqueness

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.
BUG+3The same again with three odd squares.

How often does it come up?

Our rough estimate: uncommon.

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