Avoidable Rectangle

Let us define a Deadly Pattern as a configuration of Candidates that leads to several solutions for a particular puzzle. The simplest example being a puzzle with only two unsolved Cells containing the same two Candidates: such a puzzle has two solutions. A proper Sudoku puzzle has a unique solution, thus solving a puzzle should not lead to a "Deadly Pattern".

In this strategy, we are looking for potential Deadly Patterns involving two Candidates in four Cells forming a rectangle: two Cells in two Rows and two Columns in total.

Avoidable Rectangle type 1

If three corners of the rectangle are solved Cells (not filled in with givens of the initial definition of the puzzle) with the same Candidate in one of the diagonales, then the other Candidate can not be the solution in the fourth corner; otherwise, this would lead to a Deadly Pattern.

In the example above, if candidate 5 were the solution in C8, then this would lead to a Deadly Pattern (5 and 8 could be interchanged in the rectangle). Thus candidate 5 can be eliminated in C8.

Avoidable Rectangle type 2

If two corners of the rectangle in the same Row or Column are solved Cells (not filled with givens of the initial definition of the puzzle) and the other two corners are "Bi-Value" Cells containing the same Candidates plus one other identical Candidate, then this other Candidate must be the solution in one of the "Bi-Value" Cells; otherwise, this would lead to a Deadly Pattern.

Hence the other Candidate can not be the solution in any Cell that "sees" (a Cell "sees" another Cell if both Cells belong to the same region) both "Bi-Value" Cells.

In the example above, if candidate 3 were not the solution in E5 or E9, then this would lead to a Deadly Pattern (5 and 6 could be interchanged in the rectangle). Thus candidate 3 must be the solution in either E5, or in E9, which eliminates it in Row "E".

You can practice this strategy by installing the SudokuCoach application on your Android™ device.