The XYZ-Wing is the Y-Wing with one extra candidate in the middle. A single digit added, and yet the elimination rule changes completely.
That is exactly where most solvers go wrong: they apply the Y-Wing reflex, eliminate too widely, and end up with a broken grid ten cells later.
The structure of the XYZ-Wing, why the target cells must see all three cells and not just the two pincers, the search method, and the mistake that ruins a grid.
🎬 The Domino33 video on the XYZ-Wing
Tutorial 11 covers detailed examples and the search method.
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A pivot with three candidates
The pattern is made of three cells:
- The pivot: a cell with three candidates, {X, Y, Z}
- Two pincers: two bivalue cells, {X, Z} and {Y, Z}
- Each pincer sees the pivot, but the two pincers need not see each other
The digit Z is the one found in all three cells. That is the one you will eliminate.
The difference with the Y-Wing
In a Y-Wing, the pivot is bivalue: it cannot hold Z. So you eliminate Z from every cell that sees both pincers.
Here the pivot holds Z among its three candidates. It could therefore be Z itself. A target cell must consequently see all three cells at once, pincers and pivot.
Eliminating Z from cells that see only the two pincers, as in a Y-Wing, is wrong. If the pivot is Z, those cells remain perfectly legal. It is the most widespread error on this technique, and it only shows up near the end of the grid.
A worked example
Here is a grid showing only the useful candidates:
Pivot at R2C2 {1,4,7} · pincers at R2C5 {1,7} and R3C1 {4,7} · the shared digit is the 7
The pivot R2C2 holds {1,4,7}. The pincer R2C5 holds {1,7} and sees the pivot along row 2. The pincer R3C1 holds {4,7} and sees the pivot through box 1. The 7 is present in all three.
Part 2
The three-branch reasoning
The pivot can only be 1, 4 or 7. Let us examine the three cases.
- If the pivot is 7, any cell seeing it cannot be 7.
- If the pivot is 1, the pincer R2C5, which sees the pivot, can no longer be 1: it is therefore 7.
- If the pivot is 4, the pincer R3C1, which sees the pivot, can no longer be 4: it is therefore 7.
In all three cases, the 7 lands somewhere among those three cells. A cell seeing all three therefore cannot hold a 7.
Here, two cells meet that condition: R2C1 and R2C3. They sit on row 2 like the pivot and pincer R2C5, and in box 1 like the pivot and pincer R3C1.
The 7 is eliminated from R2C1 and R2C3, the only cells seeing all three
Almost always inside the pivot's box, on the row or column linking it to one of the pincers. Look there first and you will save a great deal of time.
Part 3
The search method
Step 1, Spot the three-candidate cells
Those are your potential pivots. On a level 8 grid there are about ten of them, which stays very manageable.
Step 2, Look for two pincers around each one
For a pivot {X,Y,Z}, look in its units for two bivalue cells built only from its digits and sharing one common digit: {X,Z} and {Y,Z}. That shared digit is your Z.
Step 3, Identify the cells that see all three
This is the decisive step. Take each candidate cell and check that it shares a unit with the pivot and with each of the two pincers. If even one of the three is missing, touch nothing.
Step 4, Eliminate Z
Remove Z from those cells only. The pivot and the pincers stay untouched.
Always start from the pivot and look at its own box first. If the two pincers are not placed so that a cell of the box sees both, the pattern may exist but produces no elimination. Move to the next pivot.
🎬 See the method in action
In the video several examples are worked through on real grids, with the search method laid out step by step.
Exercise
Your turn
Here is a position with an XYZ-Wing. Only the useful candidates are shown.
Careful: the pivot holds three candidates, so the target cells must see all three cells.
Part 4
Practice quiz
Four questions to check what you have learned. Good luck!
❓ Frequently asked questions
An XYZ-Wing is made of a pivot cell with three candidates {X,Y,Z} and two bivalue cells {X,Z} and {Y,Z} that each see the pivot. The digit Z, shared by all three cells, can then be eliminated from every cell that sees the pivot and both pincers at once.
In the Y-Wing the pivot is bivalue, it cannot hold Z, and you eliminate in the cells seeing both pincers. In the XYZ-Wing the pivot holds Z among its three candidates, so it could take Z itself. Target cells must therefore see all three cells, not just the two pincers.
No. Each one only needs to see the pivot, by row, column or box. The pivot is what links them together.
Almost always inside the pivot's box, on the row or column linking it to one of the pincers. If no cell sees all three at once, the pattern exists but produces no elimination.
📋 Summary
XYZ-Wing essentials
- Setup: a pivot with 3 candidates {X,Y,Z} and two bivalue pincers {X,Z} and {Y,Z}
- Condition: each pincer sees the pivot, the pincers need not see each other
- Action: eliminate Z from the cells seeing all three cells
- The key difference: in the Y-Wing two are enough, here you need three
- Where to look: inside the pivot's box, first of all
- Related techniques: Y-Wing, W-Wing, XY-Chain
The XYZ-Wing belongs to the elaborate techniques, with the W-Wing, the Swordfish and the Sashimi X-Wing. It assumes the six basic techniques and the Y-Wing, of which it is the direct extension.
📘 Go further with the Domino33 books
The XYZ-Wing and every other technique on this site are covered step by step in the Domino33 memento, available in English.
