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Module 5 · Advanced PatternsLesson 21 of 28

XY-Wing

Identify an XY pivot and two pincers, then eliminate the shared Z candidate from common peers of the pincers.

Outcome

You can assign pivot/pincer roles to three bivalue cells, prove the shared Z under both pivot cases, and eliminate Z only from cells that see both pincers.

Intro copy

XY-Wing is easier if you stop looking for a picture and read the candidate roles:

{X,Y}
{X,Z}
{Y,Z}

The pivot chooses between X/Y.

Either choice forces one pincer to Z.

Step 1 — Build the candidate roles

Start with pivot:

{2,7}

Ask learner to choose:

  • one peer {2,Z};
  • one peer {7,Z}.

Offer several bivalue cells.

Correct construction:

  • pincer A {2,5};
  • pincer B {7,5}.

UI labels:

  • X = 2;
  • Y = 7;
  • Z = 5.

Step 2 — Prove both cases

Tap pivot = 2.

Show:

  • pincer A cannot be 2;
  • pincer A = 5.

Reset.

Tap pivot = 7.

Show:

  • pincer B = 5.

Prompt:

What is guaranteed?

Correct:

One pincer is 5.

Step 3 — Visibility test

Show four candidate-5 targets:

  1. sees both pincers;
  2. sees only A;
  3. sees only B;
  4. sees pivot + A but not B.

Prompt:

Which target can be removed?

Only #1.

Feedback:

XY-Wing elimination depends on the two pincers, not on seeing the pivot.

Step 4 — Guided board

Learner:

  1. highlights bivalue cells;
  2. chooses pivot;
  3. assigns pincers;
  4. labels Z;
  5. selects all common-peer Z targets.

No pattern roles are pre-highlighted in the final guided state.

Step 5 — False Wing

Show {2,7} pivot with:

  • {2,5};
  • {7,9}.

Prompt:

XY-Wing?

No.

Feedback:

The pincers need the same Z.

Step 6 — Naked Triple comparison

Show {2,7}, {2,5}, {7,5} all sharing one unit.

Prompt:

Which explanation is simpler here?

If the three cells collectively form a Naked Triple in that unit, accept:

Naked Triple.

Microcopy:

Different techniques can sometimes describe related candidate structures. Prefer the simplest proof that gives the move.

Practice

Include varied:

  • row/box geometry;
  • column/box geometry;
  • multiple possible pivots;
  • invalid target visibility;
  • mismatched-Z false Wing.

Hint ladder

  1. “Look at bivalue cells.”
  2. “Choose one {X,Y} pivot.”
  3. “Find {X,Z} and {Y,Z} peers.”
  4. “The pincers share Z.”
  5. “Find candidates that see both pincers.”

Completion

Four valid Wings, two false-pattern classifications, and one visibility test.

Next

XYZ-Wing

Add Z to the pivot and watch the target rule change.

Reference

Read XY-Wing for the two-case proof and connection to XY-Chains.