XY-Wing: learn the sudoku technique step by step at Sudokuen

See the technique in practice

Work through the examples step by step. Each step explains what you see in the puzzle and why the conclusion is valid.

Example:

We look at the cell at row 9, column 3. It has only two candidates left, 5 and 9. We call this cell the pivot.
Look at the neighboring cell at row 9, column 6. It shares digit 5 with the pivot and has 3 as the only other candidate.
Look at the other neighboring cell at row 9, column 7. It shares digit 9 with the pivot and also has 3 as the only other candidate.
The pivot must become either 5 or 9. If it becomes 5, the neighbor cell with the same digit cannot also have 5, so it is forced to become 3. If the pivot becomes 9 instead, the other neighbor is forced the same way to become 3. At least one of the two neighbors therefore always contains 3.
Any cell that sees both neighbors therefore cannot have 3 either. We remove it from the notes in row 9, column 5 and row 9, column 9.

We look at the cell at row 3, column 8. It has only two candidates left, 3 and 5. We call this cell the pivot.
Look at the neighboring cell at row 8, column 8. It shares digit 3 with the pivot and has 6 as the only other candidate.
Look at the other neighboring cell at row 7, column 8. It shares digit 5 with the pivot and also has 6 as the only other candidate.
The pivot must become either 3 or 5. If it becomes 3, the neighbor cell with the same digit cannot also have 3, so it is forced to become 6. If the pivot becomes 5 instead, the other neighbor is forced the same way to become 6. At least one of the two neighbors therefore always contains 6.
Any cell that sees both neighbors therefore cannot have 6 either. We remove it from the notes in row 4, column 8, row 6, column 8, row 7, column 9 and row 8, column 9.

We look at the cell at row 2, column 1. It has only two candidates left, 3 and 8. We call this cell the pivot.
Look at the neighboring cell at row 8, column 1. It shares digit 3 with the pivot and has 2 as the only other candidate.
Look at the other neighboring cell at row 3, column 1. It shares digit 8 with the pivot and also has 2 as the only other candidate.
The pivot must become either 3 or 8. If it becomes 3, the neighbor cell with the same digit cannot also have 3, so it is forced to become 2. If the pivot becomes 8 instead, the other neighbor is forced the same way to become 2. At least one of the two neighbors therefore always contains 2.
Any cell that sees both neighbors therefore cannot have 2 either. We remove it from the notes in row 1, column 1.

We look at the cell at row 3, column 6. It has only two candidates left, 6 and 9. We call this cell the pivot.
Look at the neighboring cell at row 9, column 6. It shares digit 6 with the pivot and has 4 as the only other candidate.
Look at the other neighboring cell at row 5, column 6. It shares digit 9 with the pivot and also has 4 as the only other candidate.
The pivot must become either 6 or 9. If it becomes 6, the neighbor cell with the same digit cannot also have 6, so it is forced to become 4. If the pivot becomes 9 instead, the other neighbor is forced the same way to become 4. At least one of the two neighbors therefore always contains 4.
Any cell that sees both neighbors therefore cannot have 4 either. We remove it from the notes in row 8, column 6.

We look at the cell at row 3, column 4. It has only two candidates left, 2 and 3. We call this cell the pivot.
Look at the neighboring cell at row 3, column 6. It shares digit 2 with the pivot and has 4 as the only other candidate.
Look at the other neighboring cell at row 3, column 5. It shares digit 3 with the pivot and also has 4 as the only other candidate.
The pivot must become either 2 or 3. If it becomes 2, the neighbor cell with the same digit cannot also have 2, so it is forced to become 4. If the pivot becomes 3 instead, the other neighbor is forced the same way to become 4. At least one of the two neighbors therefore always contains 4.
Any cell that sees both neighbors therefore cannot have 4 either. We remove it from the notes in row 1, column 6, row 3, column 7 and row 3, column 9.

XY-Wing consists of three cells with exactly two candidates each. The central cell, called the pivot, has candidates X and Y. Both wings see the pivot and each share one candidate with it: one wing has X and Z, while the other has Y and Z. The wings share digit Z, which is the candidate that can be removed.

The logic is a short if-then chain. If the pivot becomes X, the wing with X and Z is forced to become Z. If the pivot becomes Y, the other wing is forced the same way to become Z. One of the wings therefore becomes Z regardless, so all cells that see both wings can lose Z. Look for cells with two candidates in the same area, because three such cells close to each other are often candidates for the pattern.

Mark all cells with exactly two candidates.
Choose one of them as the pivot and call the candidates X and Y.
Look for two cells that see the pivot, where one has X and Z and the other has Y and Z.
Find the cells that see both wings, and remove Z from them.

Removing Z from cells that only see one wing. The removal requires the cell to see both wings at the same time.
Using a pivot with three candidates. Then you are into XYZ-Wing, which has stricter requirements for where the removals apply.
Removing Z from the pivot without further thought. The pivot has no Z among its candidates in a true XY-Wing, and if it does, the pattern is misidentified.

Puzzles at the Extreme level require techniques that combine three or more cells in if-then chains of logic. Work through the examples below step by step, using the same tools that the solver applies to your own puzzle.

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XY-Wing

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