W-Wing

Also called Double bivalue with conjugate link.

New to this shorthand? How to read a sudoku grid explains r4c7, houses, candidates and the rest.

What it means

Two squares far apart hold the same two numbers. A pair of homes for one of those numbers links them. Then the two squares cannot both be the other number. So anything seeing both loses it.

The exact rule, for stronger players

The rule, stated exactly: Two non-seeing bivalue cells with identical candidates {x,y}, joined by a conjugate pair on y in some house such that each of the two cells sees one end of the pair. Then x is eliminated from cells seeing both bivalue cells.

What it removes: Remove x from every cell seeing both bivalue cells.

Why it works: The conjugate pair means exactly one of its two cells is y. That forces the bivalue cell seeing it away from y, hence to x. Whichever end of the pair is y, one of the two bivalue cells is x.

Worked examples

These come from real Proven Sudoku boards. Nobody drew them by hand to make the pattern look neat. Each one is checked first, so the board is one you could really meet, the pattern is really there, and every digit it rules out is really wrong.

Sudoku grid showing W-Wing. r2c8 and r4c9 both hold only 2 and 7. If both were 7, the 2 link in r5 would have nowhere to go. So one of them is 2, and no cell seeing both can be 7. — r2c8 and r4c9 both hold only 2 and 7. If both were 7, the 2 link in r5 would have nowhere to go. So one of them is 2, and no cell seeing both can be 7.

Sudoku grid showing W-Wing. r3c1 and r9c2 both hold only 6 and 9. If both were 9, the 6 link in r6 would have nowhere to go. So one of them is 6, and no cell seeing both can be 9. — r3c1 and r9c2 both hold only 6 and 9. If both were 9, the 6 link in r6 would have nowhere to go. So one of them is 6, and no cell seeing both can be 9.

Learn these first

XY-WingThree squares, each with two numbers left.
X-ChainA chain about one number only.

Related wings

WXYZ-WingFour squares holding four numbers between them.
XYZ-WingLike the XY-Wing, but the middle square has three numbers instead of two.
Bent Naked SubsetA group of squares bent across two rows, columns or boxes.
Letter-named wings (M, S, L, H, Split, Hybrid, Local)Short chains that people gave letters to.
Remote PairsA string of squares that all hold the same two numbers, each one linked to the next.

How often does it come up?

Our rough estimate: reasonably common and often missed, because the two key cells do not see each other.

Play today's puzzle or read how difficulty is graded.