Y Wing Sudoku: One Technique, Two Names

The y wing sudoku technique and the XY-Wing are the same thing. Identical structure, identical proof, identical eliminations — two names for one pattern, and which one you meet first depends entirely on which book or app you learned from. Three cells that each hold exactly two candidates: a pivot holding {X,Y}, and two pincers holding {X,Z} and {Y,Z}, each sharing a unit with the pivot. One of the two pincers has to be Z, so any cell seeing both pincers cannot be Z.

If you arrived here searching for "Y-Wing" and found sources calling it something else, nothing has gone wrong. This page is the Y-Wing entry point. The extended reference — three more worked examples, the near-miss catalog and the XYZ-Wing comparison — lives at our XY wing sudoku guide, which is the canonical version of the same technique.

Here you get the naming story sorted out, the structure, two fully worked examples with fresh coordinates, the cases where a Y-Wing turns out to be something simpler, and the chain view that makes the pattern easier to find.

Why the technique has two names

"Y-Wing" describes the shape; "XY-Wing" describes the candidate labels. Neither name is more correct, and no solver community treats them as different techniques.

The three cells radiate from the pivot like a three-armed junction — two arms out to the pincers, and the elimination reaching down to the target. Drawn on a grid, that branching outline is roughly a Y, which is where one name comes from.

The other name comes from the notation. The pivot is written {X, Y}, and the technique is named after the two candidates that drive the case split. Sudoku programs, solver logs and most puzzle software use "XY-Wing" because it slots neatly beside XYZ-Wing, W-Wing and WXYZ-Wing in a family where the letters mean something.

There is one genuine ambiguity worth flagging. A few older texts use "Y-Wing" loosely to mean any short wing pattern, XYZ-Wing included. If a source promises an elimination and the pivot has three candidates rather than two, you are reading about an XYZ-Wing, and the target rule is stricter — the target must see all three cells, not just the two pincers.

The structure

Three cells, each with exactly two candidates, sharing three digits between them. The pivot sees both pincers; the pincers need not see each other.

"Sees" means shares a row, a column, or a 3×3 box. Across the three cells there are exactly three distinct digits, and each digit appears in exactly two of them. The pivot is the only cell without Z.

The proof takes two lines. The pivot is X or Y — there is no third option, because it is a bi-value cell.

• If the pivot is X, pincer A sees it and loses its X, so pincer A is Z.
• If the pivot is Y, pincer B sees it and loses its Y, so pincer B is Z.

At least one pincer is Z in every possible resolution of the grid. So a cell that sees both pincers is guaranteed to be looking at a Z, and cannot be one itself. You never learn which pincer holds it, and you do not need to.

Worked example: a tight Y-Wing with one target

Most Y-Wings produce a single elimination. Here is one, traced cell by cell so you can check every step.

Three bi-value cells on a stalled expert grid:

Map it to the template: X = 5, Y = 2, Z = 9.

Run the two cases.

If R6C3 = 5, then R6C7 sits in the same row and loses its 5, leaving R6C7 = 9. If R6C3 = 2, then R8C3 sits in the same column and loses its 2, leaving R8C3 = 9.

Either way, one of R6C7 and R8C3 is a 9.

Now find every cell that sees both pincers. R6C7 covers row 6, column 7 and box 6 (rows 4–6, columns 7–9). R8C3 covers row 8, column 3 and box 7 (rows 7–9, columns 1–3). Take the intersections one at a time:

Exactly one target: R8C7 cannot be 9.

If R8C7 read {3, 6, 9} before, it now reads {3, 6} — a new bi-value cell, which may well be the pivot of the next wing. If it read {6, 9}, it collapses to a naked single at 6 and the grid starts moving.

One elimination is a completely normal Y-Wing result. Do not assume you have made a mistake because the payoff looks small.

Worked example: when the pincers' boxes widen the net

A Y-Wing is worth more when each pincer's box overlaps the other pincer's line. Same three cells, five eliminations instead of one.

X = 6, Y = 1, Z = 4.

If R2C5 = 6, then R2C2 loses its 6 along row 2 and becomes 4. If R2C5 = 1, then R3C5 loses its 1 down column 5 and becomes 4. One of the pincers is a 4.

Pincer A sits in box 1 (rows 1–3, columns 1–3). Pincer B sits in box 2 (rows 1–3, columns 4–6). Those boxes are what open things up:

All five lose their 4. Three of them — R3C1, R3C2 and R3C3 — have no relationship to the pivot at all. They qualify because pincer A's box covers them and pincer B's row covers them.

The lesson generalizes: the pivot's geometry decides whether a Y-Wing exists, and the pincers' geometry decides what it is worth. Always map the full intersection rather than stopping at the first target you notice.

When a y wing sudoku pattern is really something simpler

If the two pincers see each other, the three cells form a naked triple, and the triple does more work.

Say R1C1 = {2, 5}, R1C2 = {5, 9} and R1C3 = {2, 9}. Treat R1C1 as the pivot and the other two as pincers and the Y-Wing logic holds perfectly — one of R1C2 and R1C3 is a 9, so cells seeing both lose their 9.

But those three cells sit in row 1 and in box 1 together, and their candidates pool to exactly {2, 5, 9}. That is a naked triple. It removes all three digits from the rest of row 1 and the rest of box 1, not just the 9 from a handful of cells. The Y-Wing's eliminations are a strict subset.

So the practical rule: before you trace a wing, check whether all three cells share a unit. If they do, run the naked triple instead — same cells, several times the payoff.

Two other collapses to watch for:

• The pincers have identical candidate lists. If both read {4, 9}, that is a naked pair, not a wing — there is no Z that only one of them can hold.
• Four distinct digits across the three cells. Pivot {2,5} with pincers {5,9} and {2,7} gives four digits and no shared Z. Nothing to eliminate.

The chain view, which makes them easier to find

A Y-Wing is the shortest possible XY-chain — three links — and thinking of it as a chain turns a shape-hunt into a lookup.

Chain solvers read the pattern as a walk through bi-value cells. Start at pincer A assuming it is not Z, so it is X. That forces the pivot away from X, so the pivot is Y. That forces pincer B away from Y, so pincer B is Z. Run the walk from the other end and pincer A is Z. Whichever end fails, the other end is Z — and everything seeing both ends loses it.

That reading is why the search works best as a graph problem rather than a visual scan:

1. Complete the candidate grid. Wings found against stale pencil marks are not wings.
2. Circle every bi-value cell. A stalled expert grid usually has eight to twenty. That is the entire search space.
3. For each circled cell, list the other circled cells it sees. Typically two to five.
4. Look for a pair among them that shares one digit with the pivot each, and one digit with each other. Pivot {2,5} wants a partner containing 2-plus-something and another containing 5-plus-that-same-something.
5. Confirm all three cells do not share a unit — otherwise use the naked triple.
6. Map the intersection of both pincers' units and erase Z.
7. Return to singles. One removed candidate often cascades into several placements.

Two shortcuts. A bi-value cell that sees no other bi-value cell can never be a pivot, so skip it immediately. And wings cluster where bi-value cells cluster, so start in the densest region of the grid rather than at R1C1.

Where the Y-Wing sits in the ladder

Y-Wing belongs after the fish patterns and before the chains, and it is the technique that most often rescues a grid where no fish exists.

The next technique to learn is the skyscraper. It returns to single-digit logic after the multi-digit detour of this page, and it catches the very common case where two rows nearly form an X-Wing but disagree on one column. Between a Y-Wing and a skyscraper you have coverage for most expert-level stalls.

For grid volume, our free puzzle maker generates unlimited classic 9×9 sudoku at easy, medium and hard, one to six per page with an answer key, and verifies that every puzzle has exactly one solution — which matters here, since a wing's case analysis assumes the grid is logically consistent.

Frequently asked questions

Is a Y-Wing the same as an XY-Wing?

Yes. They are two names for one technique, with the same structure, the same proof and the same eliminations. "Y-Wing" describes the branching three-armed shape on the grid; "XY-Wing" describes the pivot's two candidates, which fits the naming convention used for XYZ-Wing and WXYZ-Wing. Solver software almost always reports it as XY-Wing. Our full reference for it is the XY wing sudoku guide.

Do the two pincers need to see each other?

No — and this is the most common misconception. Each pincer must see the pivot, but the pincers themselves can sit in completely separate regions of the grid. When they do see each other, all three cells share a unit and you have a naked triple instead, which clears three digits from that unit rather than one digit from a few cells.

What is the difference between a Y-Wing and an XYZ-Wing?

The pivot. A Y-Wing pivot has exactly two candidates {X,Y}, so it can never be Z, and the elimination applies to any cell seeing both pincers. An XYZ-Wing pivot has three candidates {X,Y,Z}, so the pivot itself might be Z — which means a target has to see all three cells. XYZ-Wings occur more often but eliminate less, and their targets are usually confined to the pivot's box.

How many candidates can the y wing sudoku pattern eliminate?

Anywhere from one to about six, depending purely on geometry. If the pincers are positioned so that only one cell sees both, you get one elimination. If each pincer's box crosses the other pincer's row or column, five or six cells can lose the digit at once, as in the second worked example above. Map the whole intersection before moving on.

Is a Y-Wing a form of guessing?

No. It is a complete case analysis over two possibilities, and the conclusion holds in both branches. You never place a digit to see whether it works — you prove that at least one pincer is Z regardless of how the puzzle resolves. That is what separates wings and chains from brute-force trial and error, and it is why puzzles requiring them are still solvable by pure logic.

How often does a Y-Wing show up?

Roughly one expert or evil grid in three contains a usable one. They are rare below that level because easier puzzles resolve through singles, locked candidates and subsets before enough bi-value cells accumulate. Y-Wings appear most often in the middle-to-late stage of a hard solve, once the candidate grid has narrowed many cells to two options.