Proven Sudoku
XY-Wing
Also called Y-Wing, Bent Triple, Three-cell bivalue wing.
New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.
What it means
Three squares, each with two numbers left. The middle one shares a number with each of the other two. Whichever way the middle one goes, one of the other two ends up the same number. So any square that sees both of them loses that number.
The exact rule, for stronger players
The rule, stated exactly: Three bivalue cells: a pivot with candidates {x,y}, and two pincers with {x,z} and {y,z}, each pincer seeing the pivot. Then z is eliminated from every cell seeing both pincers.
What it removes: Remove z from every cell seeing both pincer cells.
Why it works: The pivot is x or y. If x, the first pincer is forced to z. If y, the second pincer is forced to z. Either way one pincer holds z, so no cell seeing both can.
Worked examples
These come from real Proven Sudoku boards. Nobody drew them by hand to make the pattern look neat. Each one is checked first, so the board is one you could really meet, the pattern is really there, and every digit it rules out is really wrong.
Learn these first
- Naked PairTwo squares in the same group both hold only the same two digits.
- Locked Candidates (general form)Sometimes all the spots for a digit inside one group also sit inside a second group.
Related wings
- XYZ-WingLike the XY-Wing, but the middle square has three numbers instead of two.
- Bent Naked SubsetA group of squares bent across two rows, columns or boxes.
- Letter-named wings (M, S, L, H, Split, Hybrid, Local)Short chains that people gave letters to.
- Remote PairsA string of squares that all hold the same two numbers, each one linked to the next.
- VWXYZ-WingThe same idea stretched to five squares and five numbers.
How often does it come up?
Our rough estimate: the most common wing and one of the highest-value intermediate techniques.