Lesson:XYZ-Wing
Similar to an XY-Wing, but the pivot cell has three candidates (XYZ).
💡 Interactive Board
You can interact with the board on the right at any time during the lesson to test out the concepts being explained.
← → ↑ ↓ navigate • N toggle notes • Ctrl+Z undo
💾 Progress saved locallyTap cells, use numpad →
💾 Saved locallyAbout This Lesson
XYZ-Wing is the natural extension of XY-Wing to a three-candidate pivot cell. Where XY-Wing uses a bi-value pivot with two candidates, XYZ-Wing uses a pivot containing three candidates {X, Y, Z} — and the two wings still contain {X, Z} and {Y, Z} respectively. The elimination target remains the digit Z, but the set of cells from which Z can be eliminated is different and more restricted.
The key difference from XY-Wing: in XY-Wing, eliminations apply to any cell seeing both wings. In XYZ-Wing, eliminations apply only to cells that see ALL THREE cells — both wings AND the pivot. This is because the pivot itself also contains Z as a candidate. Since Z could be in the pivot (not either wing), any elimination cell must also not see the pivot.
XYZ-Wing is rarer and harder to spot than XY-Wing, but it represents an important logical structure. It demonstrates how adding one more candidate to the pivot restricts but does not eliminate the power of wing-based reasoning.
How It Works — Step by Step
Step 1 — Find a tri-value pivot cell
Find a cell with exactly three candidates {X, Y, Z}. This is your XYZ-Wing pivot.
Step 2 — Find Wing 1 and Wing 2
Wing 1 must be in the same unit as the pivot and contain exactly {X, Z}. Wing 2 must be in the same unit as the pivot and contain exactly {Y, Z}. Both wings must see the pivot; they may or may not see each other.
Step 3 — Eliminate Z from cells seeing all three
Any cell that can simultaneously see the pivot, Wing 1, and Wing 2 cannot contain Z — because in every possible assignment of the pivot's value, Z ends up in one of the three cells (pivot or one wing). Eliminate Z from all such cells.
When to Use This Technique
XYZ-Wing is a specialist technique for hard puzzles after XY-Wing and simpler methods are exhausted. It is relatively uncommon, so do not spend too long searching for it before trying other advanced techniques.
Worked Examples
Pivot R3C5 = {1, 4, 6}. Wing 1 R3C9 = {1, 6} (same row). Wing 2 R7C5 = {4, 6} (same column). Z = 6. Any cell seeing R3C5, R3C9, AND R7C5 — which means it must be in Row 3 AND Column 5, but that is just R3C5 itself. In practice, look for cells in the same box as the pivot that also see both wings. For example, if R3C5, R3C9, and R7C5 are all visible from R3C8 (same row as Wings, same column area)... verify precisely. Remove 6 from any qualifying cell.
Frequently Asked Questions
Why is the elimination zone for XYZ-Wing smaller than XY-Wing?
Because the pivot contains Z. In XY-Wing, the pivot cannot be Z, so Z must be in one of the wings — any cell seeing both wings is safe from Z. In XYZ-Wing, Z could be in the pivot OR a wing, so elimination only applies to cells seeing all three (pivot + both wings).
Is XYZ-Wing a type of AIC?
Yes. XYZ-Wing can be expressed as a four-node AIC involving a strong link within the pivot (choosing between its three candidates strategically) and two further nodes. The AIC perspective makes the extension to longer chains natural.
Related Lessons
Ready to test your knowledge? Try applying this technique in our Expert Sudoku puzzles, Evil Sudoku challenges or explore XY-Wing technique guide. Keep training to improve your solve times and master the grid!
Ready to Practice?
Apply this technique on a real puzzle from our daily or practice modes.