A
B
C
D
E
F
G
H
I
1
5
1
4
9
1
4
7
3
2
4
9
6
8
2
2
4
7
9
6
2
4
7
8'
5
8'
9
5
9
1
2
4
7'
9
2
4
5
9
3
3
3
2
9
2
7
8'
5
6
8'
9
5
6
9
4
2
7'
9
1
2
5
4
1
2
4
1
2
4
5'
3
4
5
8
5
7
6
2
4
5
7'
9
5
8
4
5'
9
4
6'
2
4
5
6
7
9
5
6
7
9
3
4
5
7'
1
6
2
9
7
2
4
6'
1
4
5
6
9
3
8
2
4
5
2
4
5
7
2
4
2
4
8'
9
4
6
1
5
6
8'
2
4
5'
3
7
8
1
7
3
1
7
4
5
9
2
5
9
4
5'
9
8
6
9
6
2
4
8'
5
3
4
7
9
7
8'
9
1
2
4
9
2
4

WXYZ-Wing Technique

1Definition: A WXYZ-Wing consists of three cells in the same lane with four unique digits among them (the "base" cells). One of these base cells (the "pivot" cell) can also see a "pincer" cell, which contains only the base digits. If one of the digits in the pincer cell cannot see all of its matching digits in the base cells (the "non-restricted common digit: NRCD."), then that digit can be erased from cells outside of the WXYZ-Wing which see all of the NRCD's in the four WXYZ-Wing cells.
WXYZ-Wing. Yellow cells form the base: 4 digits (4,5,6,9) in 3 cells, with pivot at E6. D4 is the pincer: its 4 sees all the 4's in the base, the 5 does not, so the 5 in E5 can be erased since it sees all the 5s in all 4 cells of the wing.



2Look For: A "bent Naked Quad": four unique digits spread across four cells, where three of the cells (the "base" cells) are in the same lane or block, and the fourth cell (the "pincer") is in a different lane or block, and one of these cells (the "pivot": E6 in our example) can see all the other cells in the Wing. If one of the digits in the pincer cell cannot see all occurences of its digit in the other three cells, then that digit is the NRCD (see Consequence, below).


3Consequence: The NRCD (the digit in the pincer cell which occurs in other Wing cells that it cannot see: digit 5 in our example) can be erased from any non-Wing cell which sees all of the Wing cells.


4Why it Works: Because the NRCD occurs in Wing cells that do not see each other, that digit can conceivably occur twice in the four wing cells. So, unlike an unbent Naked Quad, the other three digits do not all have to occur in the wing cells (the NRCD's duplicative power can give us three remaining digits with two remaining cells to fit them in.) In our example, if one of the wing cells in block 2 resolved to a 5, and the pincer cell resolved to a 5, then we wouldn't need a 4 to appear in the pivot cell; it could just as easily resolve to a 6 or 9 (which means that E5 could resolve to a 4, and so cannot be erased.)


5Conversly, in every scenario, a 5 must resolve in one of the four wing cells (and threfore can be erased from any cell outside the wing cells that sees all of the wing cells: the 5 in E5 in our example.) To prove this, we can try every possible solution for the pivot cell, and we will discover that each of them eliminates the possibility that E5 could be a 5:


6Note that the pivot cell does not need to contain all four digits (as it happens to do in our first example).


7Your Turn!
There was another WXYZ-Wing in this puzzle just before the one in our example was found. Here is the puzzle just before its first WXYZ-Wing. Find the wing, and erase the candidate that the WXYZ-Wing eliminates.

Hint

See Also
Load a puzzle in Sue Doku that has an WXYZ-Wing in it.

External Links for more on WXYZ-Wings:
Click links, or press Tab to move to next parg/link, enter to highlight parg or activate link.
Or to automate.