XYZ-Wing (3-Y-Wing Unrestricted)




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:

XYZ-Wing Examples

the pivot cell(s)
the wings
the candidates we can eliminate