XYZ-Wing

Description

The XYZ-Wing is composed of 3 interconnected cells (1 anchor and 2 wings). The achor cell is connected to both of the other cells by sharing a different group with each of them.

  • The anchor cell must have exactly 3 candidates and the wing cells must have 2 candidates each.
  • Each cell must share 1 candidate with both of the other cells.
  • One candidate must be shared by all cells.
  • The non-achor/wing cells must not share a group.
  • There must be just 3 candidates in total in the 3 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 all cells MUST be in one of these cells.

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

Examples

Row Example

2 forms an XYZ-Wing in rows 1 and 2.

That means that candidates 2 can be removed from cell [2,7].

Column Example

9 forms an XYZ-Wing on columns 1 and 2.

That means that candidates 9 can be removed from cell [8,1].

Algorithm

  1. Fill in all the pencil marks in the puzzle.
  2. Find all the cells which have only 3 candidates.
  3. For every cell with only 3 candidates (potential anchor cell)
    1. Find the intersection of the peers of the anchor cell with the cells which have only 2 candidates.
    2. For every combination of these cells
      1. Check if the anchor cell is connected to both other cells by a group.
      2. Check that the non-anchor cells are NOT connected by a group.
      3. Find the digit candidate that is in common for all the cells.
      4. See if that digit is present in the intersecting cells of the peers of all 3 cells.

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 WXYZ-Wing