Y-Wing (XY-Wing)

What is a Y-Wing?

A Y-Wing (sometimes called XY-Wing) is a pattern of three cells that, together, force a single digit out of certain other cells. Each of the three cells has exactly two candidates — three different digits in total across the trio, which we will call X, Y, and Z.

The three cells split into one pivot and two wings:

• Pivot — a cell with candidates {X, Y}.
• Wing A — a cell with candidates {X, Z} that shares a row, column, or box with the pivot.
• Wing B — a cell with candidates {Y, Z} that also shares a row, column, or box with the pivot.

The conclusion: any empty cell that sees both Wing A and Wing B (shares a unit with each) cannot be Z. Z gets erased from those cells.

Why it works (the logic)

Look at the pivot. It is either X or Y — those are its only two options.

• If pivot = X, Wing A cannot be X (it shares a unit with the pivot). Wing A's only other candidate is Z. So Wing A = Z.
• If pivot = Y, Wing B cannot be Y. Wing B's only other candidate is Z. So Wing B = Z.

Either way, one of the two wings ends up holding Z. So Z definitely appears in Wing A or in Wing B. Any empty cell that shares a unit with both wings would have to be Z too — but only one Z is allowed per unit. So that cell cannot be Z.

This is one of the cleanest pieces of logic in Sudoku: a case split on a single cell forces a guaranteed conclusion three cells away.

How to spot a Y-Wing

1. Fill in pencil marks. Y-Wings are visible only after candidates are tracked.
2. Find every cell with exactly two candidates (called bivalue cells). These are your candidates for pivots and wings.
3. For each bivalue cell, treat it as the pivot. Read its two candidates {X, Y}.
4. Look at every other bivalue cell that shares a unit with the pivot. Filter to those whose candidates are {X, Z} for some new digit Z (i.e. they share X with the pivot but the other candidate is not Y).
5. For each such Wing A (with digit Z), look for a Wing B that shares a unit with the pivot and has candidates {Y, Z} — same Z.
6. Find any empty cell that sees both Wing A and Wing B and currently has Z as a candidate. That candidate gets erased.

Sounds heavy, but in practice you do this scanning by eye in 30 seconds once the shape is familiar.

A worked sketch

Imagine the pivot at R5C5 has candidates {2, 7}. Two more bivalue cells:

• R5C2 with candidates {2, 9} — shares row 5 with the pivot. This is Wing A. Common digit with pivot: 2. The other digit: 9. So Z = 9.
• R8C5 with candidates {7, 9} — shares column 5 with the pivot. This is Wing B. Common digit with pivot: 7. The other digit: 9. Matches Z = 9.

Y-Wing confirmed on digits X=2, Y=7, Z=9. Look at any empty cell that sees both R5C2 and R8C5. R8C2 is one such cell — it shares column 2 with R5C2 and row 8 with R8C5. If R8C2 currently has 9 as a candidate, that candidate is erased. The same applies to any other empty cell in the same situation.

Common beginner mistakes

• Confusing pivot and wings. The pivot is the connector — both wings see the pivot, but the wings might not see each other. The technique works as long as the geometry holds.
• Erasing Z from a wing. The wings keep all their candidates. The elimination targets third-party cells that see both wings.
• Same Z is required. Both wings must share the third digit. If one wing has Z = 9 and the other has Z = 6, no Y-Wing.
• Three different digits total. The three cells across pivot + two wings must reference exactly three distinct digits (X, Y, Z), no repeats.
• The pivot must be bivalue. A cell with three candidates is not a valid pivot for a basic Y-Wing.

When to reach for a Y-Wing

Y-Wings live in Expert puzzles. The order of attack on a hard board:

1. All singles — Naked and Hidden.
2. Pencil marks, then pairs — Naked and Hidden.
3. Intersections — Pointing Pairs and Box-Line Reduction.
4. Fish — X-Wing.
5. Chains — Y-Wing is the first chain you learn.

If a Y-Wing also fails, the puzzle wants Swordfish, XY-Chain, or one of the deeper techniques — but those are beyond this article.

Try it on a real puzzle

Open an Expert puzzle on SudokuHint, solve until the basic techniques run out, and tap the 💡 Hint button. When the engine surfaces a Y-Wing, it highlights the pivot and both wings, and shows you exactly which Z candidates are about to disappear.

Article draft v1 · pending native-speaker review