Avoidable Rectangle

An Avoidable Rectangle is a uniqueness technique — a cousin of the unique rectangle that works with digits you have already solved rather than pencil marks. It rests on a single guarantee: a well-formed Sudoku has exactly one solution. Any placement that would create a second solution must therefore be wrong, and you can strike it out on that basis alone.

The idea

Picture four cells at the corners of a rectangle that lie in two rows, two columns and two boxes. Suppose three of those corners are already filled, and they use only two different digits arranged so that the fourth corner, if it took the "matching" digit, would complete a deadly pattern: the same two digits in the same four cells, swappable without breaking any rule. If that were allowed the puzzle would have two solutions — impossible. So the fourth corner cannot take that digit, and you remove it as a candidate.

A worked example

Say r3c2 = 4, r3c6 = 6 and r7c2 = 6, all solved. These sit at three corners of a rectangle whose fourth corner is r7c6. If r7c6 were 4, the four cells would hold the 4/6 pair in a perfectly swappable square across two boxes, two rows and two columns — a deadly pattern giving two solutions. Since the real puzzle has only one, r7c6 cannot be 4. That elimination might leave r7c6 as a naked single, cascading further.

Three solved corners (4, 6, 6) form a rectangle in two boxes; the fourth can't be 4, or the 4/6 square would swap into a second solution.

Step by step

Find three solved corners of a rectangle spanning two rows, two columns and two boxes.
Check the two digits — the three corners must use exactly two values.
Identify the deadly completion — the digit that would make the fourth corner finish the swappable square.
Eliminate that digit from the fourth corner.

Common mistakes

Only two boxes will do. The four cells must sit in exactly two boxes; three or four boxes break the deadly pattern and the logic fails.
Using it on variant grids. Extra constraints — Killer cages or X-Sudoku diagonals — can forbid the swap, so uniqueness logic is unsafe there.
Forgetting it needs a unique puzzle. The whole argument assumes one solution; never apply it to a puzzle that might have several.

Which Sudoku types is this best for?

The same logic applies across variants, but it pays off more in some than others.

Great fit Classic Sudoku A clean uniqueness shortcut on Classic grids, which are guaranteed one solution. → Limited Killer Sudoku Cage constraints can break the deadly pattern, so uniqueness logic is unsafe here. → Limited Sudoku X The diagonals disrupt the deadly pattern the technique relies on. → Works Samurai Sudoku Each of the five subgrids is a standard uniquely-solved Sudoku where it still applies. →