GridWits
Expert tier Technique 15 of 21 Smart Hint: Skyscrapers and Skyscrapers+

XY-Wing

A cell with two candidates links to two other two-candidate cells that share one candidate each with it and one with each other — the shared height can't be in any cell both of those see.

How it works

  1. 1Three cells with two candidates each. The pivot in the top-left corner is {1, 2}; it shares its row with a {1, 3} cell and its column with a {2, 3} cell.
  2. 2Suppose the pivot is 1. Then the {1, 3} cell in its row can't be 1, so it's 3.
  3. 3Suppose instead the pivot is 2. Then the {2, 3} cell in its column can't be 2, so IT is 3.
  4. 4Either way one of the two wings is a 3 — we never find out which, and we don't need to.
  5. 5Any cell that sees BOTH wings therefore can't be 3. The opposite corner sees the first down its column and the second along its row. Strike its 3.
1 2 1 3 2 3 1 3 4
  • Height ruled out
  • Relationship — The arrow shows which cells support the deduction.
  • Conclusion — The final arrow lands beside the proved or ruled-out height.
Next in the ladder W-Wing →

Two cells share the same candidate pair and aren't in the same row or column, but a chain elsewhere forces one of them to one of those heights — eliminate the other height from any cell both see.