XYZ-Wing
Use a pivot with three candidates and two pincers to remove their shared digit from cells that see all three.
Pivot R2C5 (P) has three candidates: 5, 8 and 9. Pincers R2C2 (A) and R1C4 (B) each pair 5 with a different one of the pivot's other candidates. Each pincer shares a row, column or box with the pivot. If the pivot is not 5, it forces one of the pincers to be 5. At least one of these three cells must therefore contain 5. Remove candidate 5 from any other cell that shares a row, column or box with all three cells.
What to look for
Find a pivot P with exactly {X, Y, Z} and two pincers with exactly {X, Z} and {Y, Z}. The pivot must see both pincers.
Why it works
If P is X, the {X, Z} pincer must be Z. If P is Y, the {Y, Z} pincer must be Z. If P is Z, the pivot contains Z itself. No other cell that sees all three can contain Z.
Try it step by step
- Find a pivot with three candidates and two pincers with two candidates each, all using the same three digits.
- Check that the pivot shares a row, column or box with each pincer.
- Remove the pincers' shared candidate from every other cell that sees the pivot and 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: 358482 · Play this puzzle from the start
A simple example
With a pivot {1, 2, 3} and pincers {1, 3} and {2, 3}, remove candidate 3 only from other cells that see all three.
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.