# XYZ-Wing (3-Y-Wing Unrestricted)

## Difficulty

## Description

The **XYZ-Wing** is comparable to the Y-Wing in that it has a **pivot cell** and **two wings**.

The difference is that its **pivot cell is less restricted**. An XYZ-Wing configuration is therefore a bit harder two spot and reveals fewer candidates which we can eliminate.

To recap, here is a **Y-Wing**.

We can eliminate all 3 from all cells that see both wings.

Now what is that **restriction** that is applied to the Y-Wing but not the XYZ-Wing?

With **Y-Wings**, the pivot cell must ** not** hold the candidate that both wings share. (

**The pivot cell does not hold a 3.**)

**XYZ-Wings** do *not* have this restriction. Here the pivot cell may also hold the common candidate.

Since it is **less restricted** we, unfortunately, get **fewer information** out of it.

With an XYZ-Wing we can only eliminate the common candidate from the cells that see ** all** other cells involved. So we can only eliminate from the cells that see both wings

**as well as**the pivot cell.

The reasoning why this works stays the same:

Imagine any of the 3 were true, for example this one.

Then there could not be a **3** in the wings or the pivot cell.

In the pivot cells, there would only be a single candidate left, and the pivot cell would have no more candidates left, i.e. it would not have a solution.

That is why we know that the 3 cannot be the solution.

## Not spread over 4 boxes

Unlike Y-Wings, **XYZ-Wings cannot spread over 4 boxes**, which saves us some time spotting them.

- Y-Wings can stretch over the whole grid.
- XYZ-Wings can only span three boxes that are in line.

So we could find an XYZ-wing in these...

... but never in these: