Little Sudoku

Techniques › XYZ-Wing

XYZ-Wing

An XY-Wing whose pivot holds all three digits, so targets must see all three cells.

A pivot with three candidates {X,Y,Z}, and two bivalue pincers {X,Z} and {Y,Z} that it can see.

Now the Z could be in any of the three cells rather than just the two pincers — so the conclusion is weaker. A cell can only be cleared of Z if it sees all three, pivot included. In practice that usually means the whole pattern sits in one box.

A worked example

Taken from a real puzzle in our bank, at the point where this was the cheapest move available. Pattern candidates are marked in amber; anything the step eliminates is struck through in red.

5 3 4 79 27 29 8 1 6
7 2 8 6 3 1 5 9 4
6 1 9 8 5 4 7 2 3
8 6 7 1 4 5 2 3 9
3 5 1 2 9 7 4 6 8
4 9 2 3 8 6 1 5 7
2 7 6 49 1 89 3 48 5
1 4 35 57 6 38 9 78 2
9 8 35 457 27 23 6 47 1
  1. NudgeThree cells pincer digit 7: whichever way the pivot falls, one pincer takes it.
  2. WhereXYZ-Wing: r9c4, r8c4, r9c8
  3. Do itRemove r9c5 ≠ 7

How to spot it

Look for a trivalue cell with two bivalue neighbours whose candidates are both subsets of it, overlapping in exactly one digit. Then find cells seeing all three.

Practise the XYZ-Wing →

Where you will meet it

XYZ-Wing sits at tier 4 of our ladder, which means it first becomes necessary at Expert. Puzzles below that band never require it, though it may still appear as a shortcut.

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