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Y-Wing

Expert· L8
Elimination

Also known as XY-Wing / bent triple.

A Y-Wing is a tiny story with three cells — also called XY-Wing, and sometimes a bent triple (three numbers in three cells that are not in a straight line).

A pivot cell has candidates XY. It sees two wings: one is XZ, the other is YZ. The letter Z is the shared sting the pivot does *not* have.

Why it works

The pivot is either X or Y.

• If the pivot is X, then the XZ wing cannot be X — so that wing must be Z. • If the pivot is Y, then the YZ wing must be Z.

So no matter what, one of the wings becomes Z. Any cell that can see both wings would see a Z either way — it cannot be Z itself.

Contradiction view: assume a victim is Z → both wings lose Z → pivot is forced into impossibility. Same idea as a short AIC that starts and ends on Z.

How to spot it

Only scan bi-value cells. Look for a bent triple of candidates; find shared letters first, then hunt the third cell in intersections. Can span four boxes when the pivot is not boxed with a wing.

Demonstration

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Start from the rules: each of these bi-value cells must be one of its two digits. Find a pivot XY that sees two wings.

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One wing is XZ, the other is YZ — a bent triple. The sting digit Z is 1.

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World A: pivot is X → the XZ wing must be 1. World B: pivot is Y → the YZ wing must be 1.

25463798168124937537951846249587312612748938192547923478789264547829

Both stories force a wing to be 1. That pattern is a Y-Wing (XY-Wing).

25463798168124937537951846249587312612748938192547923478789264547829

Eliminate 1 from cells that see both wings (red). They get stung in every possible story. (If a victim were 1, both wings would break and the pivot would have nowhere to go.)

Example 1

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Find a bi-value pivot with two bi-value wings (bent triple).

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This Y-Wing stings with 8.

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Remove 8 from cells that see both wings (red). Both pivot cases force a wing to be that digit.

Example 2

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Find a bi-value pivot with two bi-value wings (bent triple).

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This Y-Wing stings with 1.

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Remove 1 from cells that see both wings (red). Both pivot cases force a wing to be that digit.

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