XYZ-Wing

An XYZ-Wing extends the Y-Wing pattern by using a hinge cell with three candidates instead of two. The hinge contains {X, Y, Z} and connects to two pincer cells, each containing two of these candidates.

How It Works

The Pattern

Find three cells where:

The Logic

The shared candidate Z must appear in exactly one of the three cells:

Either way, Z appears in one of the three cells. Any cell seeing all three (hinge + both pincers) cannot be Z.

Key Difference from Y-Wing

Aspect Y-Wing XYZ-Wing
Hinge 2 candidates {A, B} 3 candidates {X, Y, Z}
Pincers share C (not in hinge) Z (also in hinge)
Elimination sees Both pincers only Hinge AND both pincers

The XYZ-Wing's elimination zone is more restricted because the cell must see all three pattern cells.

How to Spot XYZ-Wings

Tri-Value Cell Focus

The key to spotting XYZ-Wings is finding tri-value cells — cells with exactly three candidates:

Step Action What to Look For
1 Find tri-value cells Cells with exactly 3 candidates
2 Check for bi-value connections Two bi-value cells that see the tri-value cell
3 Match candidates Pincers contain subsets of hinge candidates
4 Identify Z The candidate appearing in ALL three cells
5 Find eliminations Cells seeing ALL THREE pattern cells

Step-by-Step Scanning

  1. Scan for tri-value cells — These are potential hinges
  2. Check connections — Find bi-value cells that see the tri-value cell
  3. Verify pattern — Hinge {X, Y, Z}, Pincer 1 {X, Z}, Pincer 2 {Y, Z}
  4. Identify common candidate — Z appears in ALL three cells (unlike Y-Wing)
  5. Find elimination zone — Must see ALL THREE cells, not just the pincers

Key Insight: All Three Matter

Unlike Y-Wing where you only need to see both pincers, XYZ-Wing requires seeing:

This typically limits eliminations to cells in the same box as the hinge.

Example

Look for tri-value cells and ask: which cells can form an XYZ-Wing?

Pattern Analysis:

puzzle: S9B2L5X69096805722M6UA25UDQ6Y665AE601029P06DD63684HDA05D203095X63054D2D062B3P5X7903D0B99H2C042D042D2B067P9L08053H033H5M4A567H096R0805AK1M018U3K2O3A8R0J8R02BI075R0U53
mode: guided
technique: XYZ-Wing
initial:
  layers:
    hints: true
steps:
  - text: >
      XYZ-Wing starts with a tri-value cell (three candidates). R4C7 has {1, 2, 7} — a potential pivot.
    hint: subtle
    technique: XYZ
    state:
      selection:
        cells: [R4C7]

  - text: >
      Find two bi-value cells connected to the pivot. R4C9 {1, 7} and R5C8 {2, 7} both see R4C7.
    hint: obvious
    technique: XYZ
    state:
      selection:
        cells: [R4C7, R4C9, R5C8]

  - text: >
      The common candidate 7 appears in ALL three cells — pivot AND both pincers.
    hint: obvious
    technique: XYZ
    state:
      selection:
        cells: [R4C7, R4C9, R5C8]

  - text: >
      Eliminate 7 from cells seeing ALL THREE pattern cells. R5C7 and R6C7 see all three, so R5C7~7 and R6C7~7.
    hint: detailed
    technique: XYZ
    state:
      selection:
        cells: [R5C7, R6C7]
settings:
  showCandidates: true
  showControls: true
  showDescription: true
  navigation: numbered

Finding Elimination Cells

For XYZ-Wing eliminations, the target cell must see:

  1. The hinge (via row, column, or box)
  2. Pincer 1 (via row, column, or box)
  3. Pincer 2 (via row, column, or box)

This typically limits eliminations to cells in the same box as the hinge when the pincers are outside.

Tips

  1. Start with tri-value cells — Look for cells with exactly three candidates
  2. Check for matching pincers — Both pincers must share the "Z" candidate with the hinge
  3. Limited elimination zone — Usually only 1-2 cells can see all three
  4. Often in boxes — The hinge is frequently connected to one pincer via box

The Wing Family

Wing Hinge Candidates Pincers Elimination Zone
Y-Wing 2 2 bi-value cells Sees both pincers
XYZ-Wing 3 2 bi-value cells Sees all three cells
WXYZ-Wing 4 3 cells Sees all four cells

More Puzzles

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