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Sudoku guide

Sudoku best practices

Tips for playing well, the most useful first.

  1. Start with the rows, columns and boxes that are nearly full. One with a single empty cell takes the one digit it's missing; with two or three empty, check where each missing digit can go.
  2. Pick a digit and look along three boxes side by side. Where it already sits in two of them, it blocks two rows, so in the third box it must go in the row that's left, often in just one cell. Then do the same down the columns.
  3. When scanning finds nothing more, write every candidate into each empty cell as notes. A cell left with only one candidate takes that digit.
  4. Each time you place a digit, cross it out of the notes in its row, column and box, then look nearby again. One placement often leaves a new single next to it.
  5. If a digit's candidates in a box all sit in one row or column, the digit must go on that line inside the box. Cross it out of the rest of that row or column.
  6. The reverse works too: if a digit's candidates in a row or column all sit in one box, cross it out of the rest of that box.
  7. Two cells in one row, column or box with the same two candidates, and nothing else, hold those two digits between them. Cross both digits out of the other cells there.
  8. If two digits can only go in the same two cells of a row, column or box, those cells hold them. Clear every other candidate from those two cells.
  9. The same idea grows to three: three cells in one row, column or box whose candidates, taken together, are only three digits hold those three digits, so cross them out everywhere else there.
  10. X-Wing: when a digit has exactly two places in each of two rows, and they line up in the same two columns, it takes opposite corners of that rectangle. Cross it out of the rest of both columns. It works with rows and columns swapped, too.
  11. XY-Wing: find a cell with two candidates, say 1 and 2, that sees a cell with 1 and 3 and another with 2 and 3. Whichever digit the first cell takes, one of the other two is a 3, so any cell that sees both of them can't be a 3.
  12. Never guess. Every puzzle here has exactly one solution that logic reaches, so when you're stuck there's always a technique still to find.
  13. When you take a hint, read which technique it names and why it works, not only which cell it fills. Then look for the same pattern yourself in your next puzzle.