Grafite Sudoku
The XY-Wing in sudoku
The XY-Wing uses three cells with exactly two pencil marks each. One is the pivot, the other two are the wings.
The pattern
- The pivot has candidates X and Y.
- One wing, which sees the pivot, has X and Z.
- The other wing, which also sees the pivot, has Y and Z.
If the pivot is X, the first wing becomes Z. If the pivot is Y, the second wing becomes Z. Either way one of the wings is Z, so any cell that sees both wings cannot be Z.
In the example the pivot in row 5, column 5 has 2 and 7. The wing in row 5, column 1 has 2 and 9; the wing in row 2, column 5 has 7 and 9. The cell in row 2, column 1 sees both wings: 9 is removed from its pencil marks.
How to find it
Look for cells with only two candidates and check which ones see each other. It is a technique for hard sudoku: try it when pairs and locked candidates give nothing more.
In the app: "XY-Wing" lesson in the Sudoku Academy
In the Sudoku Academy of Grafite Sudoku this technique is an interactive lesson on the grid, with exercises from real puzzles.