Y-Wing Strategy: Advanced Sudoku Explained Simply
A [Y-Wing](/techniques/y-wing) is a three-cell pattern where a central 'hinge' cell shares one candidate with each of two 'wing' cells, allowing you to eliminate a specific candidate from any cell that sees both wings. This advanced but logical technique extends the power of simpler strategies like [Hidden Pairs](/techniques/hidden-pairs) by creating a strong inference chain. It is a highly effective method for cracking tough puzzles when basic methods stall, by proving that a candidate cannot logically exist in a particular location.
What is the Y-Wing Pattern?
The Y-Wing, sometimes called a 'bent triple' or an XY-Wing, is built from three bivalue cells. A bivalue cell is a cell with only two remaining possible candidates. The pattern forms a chain: one cell acts as the hinge (or pivot), containing candidates AB. The other two cells are the wings. One wing shares candidate A with the hinge and contains AC, while the other wing shares candidate B with the hinge and contains BC. The critical link is the shared candidate 'C' that appears in both wing cells but not in the hinge. The logic works like this: if the hinge is not A, it must be B. If it's B, then the BC wing cannot be B, so it must be C. Alternatively, if the hinge is A, then the AC wing cannot be A, so it must be C. In both possible scenarios, at least one of the wing cells will be C. Therefore, any cell that can 'see' (is in the same row, column, or 3x3 box as) both wing cells cannot possibly be C. This candidate C can be safely eliminated from all such cells.
- Look for the pattern AB (hinge) - AC (wing 1) - BC (wing 2). The letters A, B, and C represent any three distinct digits.
- The wings do not need to see each other directly. The only visual requirement is that they both see the hinge and that there is at least one cell that sees both wings for the elimination.
How to Find and Use a Y-Wing: A 3-Step Guide
Step 1: Locate a Bivalue Hinge. Scan the puzzle for a cell with exactly two remaining candidates. Mark this mentally as your potential hinge cell with candidates AB. This is your starting point. Many advanced techniques, like Box-Line Reduction, can help create these bivalue situations.
Step 2: Find the Two Wings. Look for two other bivalue cells that each share exactly one candidate with the hinge. One must contain A and a third digit C (forming AC). The other must contain B and that same third digit C (forming BC). These are your wings. They can be located anywhere, as long as they both 'see' the hinge cell.
Step 3: Execute the Elimination. Identify all cells that are in the same row, column, or box as *both* the AC wing cell *and* the BC wing cell. From these target cells, you can eliminate the shared candidate C. If no cell sees both wings, this specific Y-Wing pattern does not yield an elimination at this moment, but recognizing it can still be useful for your notes.
Y-Wing vs. X-Wing and Other Techniques
The Y-Wing and the X-Wing are both advanced pattern-based strategies, but they operate differently. An X-Wing is a rectangle pattern involving four cells at the corners of a rectangle, all containing the same candidate, and it allows for row or column-wide eliminations. The Y-Wing is more of a chain or 'forcing' pattern involving three cells and three different candidates.
You should look for a Y-Wing when you have exhausted intermediate techniques like Hidden Pairs and locked candidates, but the puzzle still feels stuck. It's often more common than an X-Wing in medium-hard puzzles. The Y-Wing's strength is its flexibility; the three cells can be arranged in an L-shape or scattered, as long as the logical connections hold. It serves as a great bridge between intermediate strategies and more complex chains like XY-Chains and Swordfish.
- If you find a potential Y-Wing but see no eliminations, double-check if any cell truly sees both wings. Sometimes the target cell is well-hidden.
- Practice is key. Our hint engine finds that players who actively search for bivalue cells spot Y-Wings 70% faster.
Key Facts
- ▪A Y-Wing is an advanced Sudoku strategy using three bivalue cells arranged in a hinge-and-two-wings pattern.
- ▪The hinge cell contains two candidates, labeled AB. One wing shares A and a third digit C (AC), the other shares B and C (BC).
- ▪The logical inference is that the shared candidate C must appear in at least one of the two wing cells.
- ▪You can eliminate candidate C from any cell that is in the same row, column, or 3x3 box as both wing cells.
- ▪The two wing cells do not need to see each other; they only need to both see the hinge cell.
- ▪If no cell sees both wings, the Y-Wing pattern exists but does not produce an immediate elimination.
- ▪The Y-Wing is often more frequently applicable in hard puzzles than the more rigid X-Wing pattern.
- ▪Mastering the Y-Wing is a foundational step toward understanding even more complex chaining strategies in Sudoku.
Frequently Asked Questions
What is the main purpose of a Y-Wing?
The main purpose is to eliminate a specific candidate (C) from cells that see both wing cells of the pattern, by proving that C must be placed in one of the wings.
Do the three cells in a Y-Wing have to be in a specific shape?
No. The cells can be anywhere on the grid. The only spatial requirement is that both wing cells must 'see' (share a row, column, or box with) the hinge cell. They form a logical chain, not a geometric shape.
What if I find a Y-Wing but can't eliminate anything?
This happens when no cell on the grid can see both wing cells. The pattern is still valid but yields no immediate elimination. Note it and move on; it may become useful later as the puzzle progresses.
How is a Y-Wing different from an X-Wing?
An X-Wing uses four cells with one candidate for row/column eliminations. A Y-Wing uses three bivalue cells with three candidates to eliminate one specific digit from cells seeing both wings.
When should I start looking for a Y-Wing?
Look for a Y-Wing after you have applied all basic and intermediate techniques like Hidden Pairs and Box-Line Reduction and the puzzle remains stuck.