How to Solve Sudoku: XYZ-Wing

A pivot with notes {A,B,C} and the 2 cells it sees, {A,C} and {B,C}. Then C can be removed from any cell that sees all 3.

On Puzzle Lounge it appears at Master.

See it step by step

  1. A board full of notes. Look at the cells with few notes (the small digits are the notes, or candidates)
  2. This cell is 2, 8 or 9 (we call it the pivot)
  3. The 2 cells the pivot sees are {2,9} and {8,9} (cells in the same row, column or box)
  4. If the pivot is 2, this cell is 9
  5. If the pivot is 8, this cell is 9
  6. If the pivot is 9, the pivot itself is 9
  7. In every case, one of the 3 cells is 9
  8. So a 9 that sees all 3 cells can be removed (9 goes from row 1, column 5)

This is Master No.13, partly solved.

Solve this puzzle →

How to find it

  1. Find a cell with 3 candidates and make it a possible pivot.
  2. Among the cells the pivot sees, find 2 cells whose candidates are just 2 of the pivot's 3. The digit those 2 cells share is C.
  3. See whether C is in any cell that sees all 3 cells (usually in the same box as the pivot).

Things to watch

  • Unlike the XY-Wing, the cell you remove from must also see the pivot.
  • The candidates of both of the 2 pincers must lie within the pivot's candidates.
Read the full explanation

When a cell with candidates {A, B, C} (the pivot) sees the 2 cells {A, C} and {B, C}, one of the 3 cells must be C. So C can be removed from any cell that sees all 3.

It is an XY-Wing whose pivot has 3 candidates. Suppose the pivot is {A, B, C} and the 2 cells it sees (the pincers) are {A, C} and {B, C}.

If the pivot is A, the {A, C} cell is C. If the pivot is B, the {B, C} cell is C. If the pivot is C, it is C itself. In every case, C goes in one of the 3 cells.

So C cannot go in any cell that sees all 3 cells: the pivot and its 2 pincers.

The pivot, row 2, column 5, is {2, 8, 9}; the pincers, row 4, column 5 and row 1, column 4, are {2, 9} and {8, 9}. Whichever digit the pivot is, one of the 3 cells is 9. So 9 can be removed from the candidates at row 1, column 5, which sees all 3.

Other techniques

Hidden SingleNaked SinglePointingClaimingHidden PairHidden TripleCage Combinations (Killer)Rule of 45 (Killer)Naked PairNaked TripleX-WingXY-WingSwordfishSkyscraper2-String KiteW-WingJellyfish

For the basics and how to use notes, see how to solve sudoku, with tips. If you get stuck, the game's hints guide you step by step, starting with where to look.

Solve sudoku (free, no download) →