Description

The WXYZ-Wing is composed of 4 interconnected cells. This is similar to XY-Wing and XYZ-Wing, except with 4 cells.

• The anchor cell must have 3 or 4 candidates and the non-anchor cells must have 2 or 3 candidates each.
• Each cell must share 1 candidate with the other cells.
• There must be just 4 candidates in total in the 4 cells.

Reasoning

Because the cells are connected both by sharing a group with the achor cell and 1 candidate with each other, it means that the candidate in common between the wing cells MUST be in one of these cells.

That implies that the cells which are in the intersection of the peers of the all the wing cells, cannot have their shared candidate as a possible value.

Examples

Type I

9 forms a WXYZ-Wing in rows 3 and 5.

That means that candidate 9 can be removed from cell [4,2].

Type II

8 forms a WXYZ-Wing on rows 8 and 9.

That means that candidate 8 can be removed from cell [9,2].

Type III

9 forms a WXYZ-Wing on columns 2 and 3.

That means that candidates 9 can be removed from cell [9,1].

Algorithm

1. Fill in all the pencil marks in the puzzle.
2. Find 4 cells that have exactly 4 candidates combined.
3. Find the anchor cell which is connected to all other cells and share a candidate.
4. Find the wing cells that are in the same region as the anchor.
5. Find the wing cells which are in a different region from the anchor, but in the same row or column.
6. The shared candidate between the wing cells can be removed from the intersection of the peers of the cells which contain the candidate.

Practice Puzzles

If you tap on the following links on an iOS device which has the Sudoku Tutor app installed, it will launch the app and open the practice puzzle. Tap hint once the puzzle is open to see the strategy in action.

Sample Puzzle 1
Sample Puzzle 2
Sample Puzzle 3

Next Step

Back to Sudoku Solvers or continue to next algorithm Swordfish