Variant Sudoku

XYZ-Wing

A middle cell with candidates ABC sees two wings, AC and BC. One of the three cells must be C, so a cell that sees all three can’t be C.

5
1
2
5
1
9
2
5
7
3
128
28
9
5
5
12689
7
3
9
4
7
3
2
8
3
9
4
6
3
4
9
12
6
8
5
7
9
8
4
5
1
2
3
Clear 2 from cells that see all three.

Why it works

On the board above:

r4c5 can be 1, 8 or 2. r8c5 is 1 or 2, and r4c6 is 8 or 2.

If r4c5 is 1, then r8c5 is 2. If it is 8, then r4c6 is 2. If it is 2, it is 2 itself.

So one of the three cells is 2. r5c5 sees all three, so it can’t be 2.

How to spot it

  1. Find a middle cell with three candidates

    Call them A, B and C.

  2. Find two wings it sees

    Each wing has two of the middle’s digits, and both wings hold C.

  3. Look for cells that see all three

    These are almost always in the middle cell’s box.

  4. Clear C from them

    Only those cells lose C.

Practice

Real boards from the solver, with every pencil mark filled in. Spot it, then use it, then find it cold.

Loading the boards…

Try it in a real puzzle

Each of these needs an XYZ-Wing to finish. It opens in the player.

Tips

Fewer cells to clear

Because the cleared cell must see all three, an XYZ-Wing usually clears only one or two cells.

Start in a box

Look for a three-mark cell that shares a box with a two-mark wing.

W-WingTwo matching two-candidate cells, linked through a digit with only two spots, force the other digit into one of them.Next: W-Wing →

In the glossary