Broken Wing

A Broken Wing is a single-digit pattern similar to a Turbot Fish.

It is also a solving technique that uses this pattern.

How it works

A correct Sudoku cannot contain a closed loop with an odd number of strong links. Every candidate would contradict itself when the implications through the loop are followed. When a single-digit pattern is present that is almost a closed loop, the grid must contain one or more candidates that prevent this pattern from forming an odd-sized, strong links only loop. These candidates are the guardians. One of these guardians must be true, which is the premise for this technique. Several logical deductions can be made using this premise.

Single Guardian

Here is an example of a pattern that contains only a single guardian:

Broken Wing , Sudoku solving technique

The cells marked with X forms a loop r5c2 - r2c2 - r2c5 - r1c6 - r5c6 which already has 4 strong links. The dashes mark the cells that do not contain any candidates for this digit. If the guardian G in r5c8 were removed, the loop of 5 strong links would be closed, making the puzzle invalid. As a result, we can place the selected digit in the single guardian.

Multiple Guardians

Here is a pattern that contains 2 guardians:

Broken Wing ,How to solve sudoku puzzles - Solving sudoku strategy

The same loop forms the basis. Now there are 2 guardians, both in column 8. We know that at least one of them must be true. Therefore we can eliminate the remaining candidates for this digit from column 8 (the * cells).

Broken Wing , Sudoku solving technique

It is also possible to use the guardians to eliminate the cells that are part of the loop.

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