XY-Wing
A pivot with two candidates connects two pincers. At least one pincer must contain their shared digit.
Pivot R8C2 (P) can contain only 2 or 3. Pincers R8C9 (A) and R7C1 (B) each have two candidates: 4 and one of the pivot's digits, a different one in each. Each pincer shares a row, column or box with the pivot. Whichever digit goes in the pivot, one of the pincers must contain 4. Remove candidate 4 from any other cell that shares a row, column or box with both pincers.
What to look for
Find three cells with exactly two candidates each: a pivot P {X, Y}, a pincer A {X, Z} and a pincer B {Y, Z}. The pivot must see both pincers, but the pincers do not need to see each other. This pattern is also known as a Y-Wing.
Why it works
If P is X, A must be Z. If P is Y, B must be Z. Either way, at least one pincer contains Z, so no other cell that sees both pincers can contain Z.
Try it step by step
- Find three cells with candidate sets {X, Y}, {X, Z} and {Y, Z}.
- Check that the {X, Y} pivot shares a row, column or box with each pincer.
- Remove candidate Z from every other cell that sees both pincers.
Try it on a real puzzle
Start with the highlighted step, then keep solving. Use "Apply hint" to make the suggested change, or enter your own digits and candidate notes. Use "Undo" to reverse your last change.
| C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | |
|---|---|---|---|---|---|---|---|---|---|
| R1 | |||||||||
| R2 | |||||||||
| R3 | |||||||||
| R4 | |||||||||
| R5 | |||||||||
| R6 | |||||||||
| R7 | |||||||||
| R8 | |||||||||
| R9 |
Use the arrow keys to move, 1-9 to enter a digit and Backspace or Delete to clear a cell. To add or remove a candidate, press C and then 1-9.
Source puzzle number: 136813 · Play this puzzle from the start
A simple example
With a pivot {1, 2} and pincers {1, 3} and {2, 3}, remove candidate 3 from any other cell that sees both pincers.
A house is a row, column or 3 × 3 box. A line is a row or column. Two cells "see" each other when they share a house. R1C3 means row 1, column 3. Boxes are numbered 1-9 from left to right and top to bottom. Braces such as {1, 2} show a cell's candidates, not confirmed digits.