A cell with two candidates, the pivot, sees two other cells with two candidates, the wings. Each wing shares a different one of the pivot's digits, and both wings carry the same third digit. Whichever digit the pivot takes, one wing ends up with the third digit, so any cell that sees both wings loses it.
How to spot it
The fish read one digit across several rows. A Y-wing reads cells instead. It needs three of them, each with exactly two candidates.
Pick a cell with two candidates, say A and B. That is the pivot. Among the cells it sees, look for one with two candidates, A and some other digit C. Then look for another with B and the same C. Those two are the wings. Each wing has to see the pivot. The wings do not have to see each other.
Last, find the cells that see both wings. Any C in them can go. Late in a puzzle many cells are down to two candidates, so there are plenty of pivots to try.
Pick a pivot with two candidates
Row one has three empty cells, and each has two candidates. The cell in column five has 8 and 9. Take it as the pivot. Whatever else happens, it ends up as one of those two.
Find a wing for each of its digits
The pivot sees the cell in column seven of its own row, which has 5 and 9. It also sees the cell in row nine of its own column, which has 5 and 8. One shares the 9, the other shares the 8, and both have a 5 as their second digit. That makes a Y-wing on 5. The cell in row three, column four also sees the pivot and has an 8, but its other digit is 1, so it does not pair with the cell in row one.
Follow both of the pivot's digits
If the pivot is 8, the wing in row nine shares its column and cannot be 8, so it is 5. If the pivot is 9, the wing in row one shares its row and cannot be 9, so that wing is 5. The pivot has no third option. One of the two wings holds the 5, and you do not need to know which.
Strike the 5 from cells that see both wings
A cell that sees both wings would share a house with that 5 in either case, so it cannot be 5. The wing in row one covers row one, column seven and its box. The wing in row nine covers row nine, column five and its box. Only one empty cell sits in both reaches, in row nine, column seven. It loses its 5. The pivot sits at the other crossing, but it has no 5 to lose.
Read what the strike left behind
The cell in row nine, column seven had 5 and 9. Now it is a 9, a naked single. Before the strike this grid had no single of either kind. Nothing earlier on the path removed a mark either, from pointing pairs through to the jellyfish. The Y-wing is the first technique that does anything here.
Why either case is enough
The argument splits on the pivot. It has two candidates, so it is one or the other. Each choice takes that digit away from one wing, and a cell with two candidates that loses one is left with the other. So each choice puts a 5 into a wing. A cell that sees both wings sees that 5, whichever wing it is in.
This is why each wing must share a different digit with the pivot. If both shared the 9, a pivot of 8 would leave them both alone, and nothing would follow.
On this grid the pivot is 9, so the 5 goes in the wing in row one. The strike did not depend on it.
The three cells can also sit in one house. Row one's empty cells hold 5 and 8, 8 and 9, and 5 and 9, which is a Y-wing with all three cells in the same row. Three cells sharing three digits in one house are a naked triple, which comes earlier on the path. This one strikes nothing, because row one has no other empty cells.
Two wings on the same digit
Go back to the board before the strike and take the cell in row nine, column seven as a pivot. It has 5 and 9. The cell in column five of the same row has 5 and 8. So does the cell in row eight, column nine, in the same box. Two cells with two candidates, both seeing the pivot and both carrying an 8, look like wings.
They are not, because both hang on the 5. If the pivot is 5, both become 8. If the pivot is 9, neither is forced, and on this grid both turn out to be 5. Treat it as a Y-wing anyway and you would strike the 8 from row eight, column four and from row nine, column eight. Both of those cells are 8.
Before you strike, check that each wing shares a different digit with the pivot.
The pivot has 8 and 9. One wing shares the 9, the other the 8, and both carry a 5. Each case puts a 5 in a wing.
The pivot has 5 and 9. Both wings share the 5 and carry an 8. A pivot of 9 forces neither wing, so nothing can be struck.
The same four corners, another pivot
The pivot and its wings sit at three corners of a rectangle, on rows one and nine and columns five and seven. The fourth corner is the cell the strike hit. On the board before the strike, the corner in row nine, column five works as a pivot too. It has 5 and 8. The old pivot in row one is now a wing on the 8, and the corner in row nine, column seven is a wing on the 5. Both carry a 9, and the one cell that sees both is row one, column seven. That cell loses its 9.
The two strikes agree. Row nine, column seven is 9 and row one, column seven is 5, as they must be, since they share a column.
Look at cells with two candidates first. Take one as the pivot and find two cells it sees, also with two candidates, one sharing each of its digits and both carrying the same third digit. Strike that digit from every cell that sees both wings. If the wings share the same pivot digit, there is nothing to strike.
Where this sits on the path
A Y-wing places nothing. It removes candidates and leaves the placing to the singles. On the grid above it made one naked single, in row nine.
It opens the wings, the chapter after the fish. A fish follows one digit across rows and columns. A wing works with a few cells and the digits inside them, and the reasoning is a split. The pivot is one digit or the other, and both lead to the same strike.
The XYZ-wing comes next. Its pivot has three candidates instead of two. A Y-wing is also the shortest XY-chain, made of the pivot and its two wings.
On the same board, the cell in row three, column one has 5 and 8. It sees the cell in row three, column nine, with 5 and 9, and the cell in row four, column one, with 8 and 9. Which 9 can you strike?
List the houses each wing covers. The strike lands only where both reach.
Recap
- Look for
- A pivot with two candidates that sees two wings with two candidates each. Each wing shares a different pivot digit, and both carry the same third digit.
- Scope
- Every cell that sees both wings. The pivot and the wings keep their candidates.
- Result
- The third digit comes out of every cell that sees both wings.
- Tell-tale
- Late in a puzzle, with many cells down to two candidates and the same few digits in them.
- If it fails
- If both wings share the same pivot digit, or their other digits differ, there is no Y-wing. Try another pivot, or look for a pivot with three candidates, which is the XYZ-wing.