How to Solve Sudoku: Swordfish

The X-Wing with 3 lines. If, in 3 rows, the places for a digit fit in the same 3 columns, it can be removed from the other cells of those 3 columns.

On Puzzle Lounge it appears from Oni up.

See it step by step

  1. A board full of notes. Look only at the 5s (the small digits are the notes, or candidates)
  2. ● = a cell where 5 can go (notes other than 5 have been removed)
  3. In row 3, 5 is only in columns 6 and 7
  4. Row 8 is in columns 3 and 6, row 9 in columns 3, 6 and 7 (the ● of 3 rows fit in 3 columns)
  5. 5 can only go in these 3 ways (each puts one in columns 3, 6 and 7)
  6. In every case, the 5s of columns 3, 6 and 7 are in these 3 rows
  7. So the other 5s can be removed (5 goes from row 7, column 7)

This is Oni No.135, partly solved.

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How to find it

  1. Pick a digit and list the rows where it has only 2 to 3 candidates.
  2. Among them, find 3 rows whose candidates fit in 3 columns in all.
  3. If you find them, remove the digit from the other cells of those 3 columns.

Things to watch

  • A row need not have all 3 candidates (2 is fine).
  • When you cannot find an X-Wing, widening the search to 3 lines for the same digit sometimes finds one.
Read the full explanation

This is the 3-column version of the X-Wing. If a digit's candidates, in 3 rows, all lie within the same 3 columns, the digit can be removed from the other rows of those 3 columns.

Suppose a digit's candidates, in each of rows A, B and C, lie only in columns X, Y and Z (2 or 3 places in each row).

The digit goes once in each of the 3 rows, so it goes once in each of columns X, Y and Z.

So the digit cannot go in the other rows of columns X, Y and Z.

In rows 3, 8 and 9, the candidates for 5 lie only in columns 3, 6 and 7. So the 5s of columns 3, 6 and 7 are used up in these 3 rows, and 5 can be removed from the candidates at row 7, column 7.

Other techniques

Hidden SingleNaked SinglePointingClaimingHidden PairHidden TripleCage Combinations (Killer)Rule of 45 (Killer)Naked PairNaked TripleX-WingXY-WingSkyscraper2-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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