Three two-candidate cells form a loop → erase from any cell that sees both wings.
Technique 11 in the order the hint searches · difficultyExpert · up to advanced techniques
It uses three cells with exactly two candidates each. Say the pivot is 1·5, one wing is 1·2, the other is 5·2, and the pivot can see both wings. If the pivot is 1 the first wing is 2; if it is 5 the second wing is 2. Either way, one of the wings is a 2.
Take a two-candidate cell as your pivot
Pick a cell with two candidates, then among the cells it can see look for ones that also hold two candidates and share exactly one digit each. The two wings need not see each other — which is how three widely separated cells end up linked.
This is how the hint puts it
r4c7 holds only 1 and 7, r5c9 only 7 and 8, r9c7 only 1 and 8. If r4c7 is 1 then r5c9 is 8; if it is 7 then r9c7 is 8 — either way one of the two is 8, so 8 comes off any cell that sees both.
Whatever the pivot turns out to be, one wing is that digit
The pivot has only two possible values, and in both cases one of the wings becomes that digit. You don't know which case is true, but you do know one of the two is. So any cell that sees both wings cannot be that digit.
From here on these are the advanced techniques that make a puzzle Expert. Measured over 200 puzzles it was the deciding move five times — more often, in fact, than X-Wing.
Puzzles where this technique decides it
Four puzzles that won't give up the next move until you reach Y-Wing (XY-Wing). Press a number to open it.
- Practice 1 ·
4-9435761 - Practice 2 ·
4-8871522 - Practice 3 ·
4-2045006 - Practice 4 ·
4-8788050