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:
- sees both pincers;
- sees only A;
- sees only B;
- 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:
- highlights bivalue cells;
- chooses pivot;
- assigns pincers;
- labels Z;
- 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
- “Look at bivalue cells.”
- “Choose one
{X,Y}pivot.” - “Find
{X,Z}and{Y,Z}peers.” - “The pincers share Z.”
- “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.