How to Solve Sudoku: XY-Wing

3 cells with 2 notes each, in the pattern {A,B}, {A,C}, {B,C}. Then C can be removed from any cell that sees both ends.

Also called a Y-Wing. On Puzzle Lounge it appears from Oni up.

See it step by step

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

This is Oni No.1, partly solved.

Solve this puzzle →Print and solve →

How to find it

  1. Mark the cells with only 2 candidates.
  2. Take one of them as the pivot, and find 2 cells (in the same column, row or box) that each share one digit with the pivot.
  3. Remove C, the other digit the 2 pincers share, from any cell both pincers see.

Things to watch

  • All 3 cells must have exactly 2 candidates.
  • The pincers do not need to see each other. It works as long as the pivot sees them.
Read the full explanation

When 3 cells with 2 candidates each form the pattern {A, B}, {A, C}, {B, C}, and the middle {A, B} cell sees the other 2 cells, C cannot go in any cell that sees both of the 2 end cells.

Suppose the middle cell (the pivot) has candidates {A, B}, and the 2 cells it sees (the pincers) have {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. Either way, one of the pincers must be C.

So C cannot go in any cell that both pincers see.

The pivot, row 2, column 8, is {4, 5}; the pincers, row 2, column 6 and row 3, column 7, are {3, 4} and {3, 5}. Whichever digit the pivot is, one of the pincers is 3. So 3 can be removed from the candidates at row 3, column 5, which both pincers see.

Other techniques

Hidden SingleNaked SinglePointingClaimingHidden PairHidden TripleCage Combinations (Killer)Rule of 45 (Killer)Naked PairNaked TripleX-WingSwordfishSkyscraper2-String KiteXYZ-WingW-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.

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