Sudoku solving techniques
These are twelve Sudoku solving techniques, in the order to learn them. The first five are the ones our Sudoku uses to grade every puzzle it deals: the game solves each grid the way a person would, trying the simplest deduction first, and the hardest of those five it needs decides whether the puzzle is Easy, Medium or Hard. Their worked examples are taken at the exact moment the game’s own solver needed that technique.
The other seven are what Expert puzzles ask for. Our game’s solver does not use them — a grid it cannot finish with the first five is rated Expert — so their examples are positions from Expert puzzles our generator dealt, where we checked that nothing simpler moves the grid forward. Either way, each example is one you could meet in your next game.
In learning order
- Naked single A cell where eight digits are already ruled out, so only one can go there.
- Hidden single A digit with only one possible home in a row, column or box.
- Pointing pair A box whose only spots for a digit lie on one line clears that digit from the rest of the line.
- Box-line reduction A line whose only spots for a digit lie in one box clears that digit from the rest of the box.
- Naked pair Two cells in one unit with the same two candidates own both digits.
- Hidden pair Two digits confined to the same two cells of a unit clear every other candidate from those cells.
- Naked triple Three cells in one unit holding only three digits between them own those digits.
- Hidden triple Three digits confined to the same three cells of a unit clear everything else from those cells.
- X-Wing One digit confined to the same two columns in two rows is cleared from the rest of those columns.
- XY-Wing A two-candidate pivot and two pincers force a shared digit into one pincer, clearing it where they cross.
- Swordfish An X-Wing on three lines: one digit confined to three columns across three rows.
- XYZ-Wing An XY-Wing whose pivot has three candidates; the shared digit leaves cells that see all three cells.
What each difficulty level needs
- Easy
- Naked singles only, from start to finish.
- Medium
- Hidden singles as well: naked singles alone stall part-way.
- Hard
- At least one pointing pair, box-line reduction or naked pair once both kinds of single run out.
- Expert
- More than the first five: our solver cannot finish an Expert grid with them alone. In 3,000 Expert puzzles we measured, the hardest technique needed was a hidden pair in 5.7%, an XY-Wing in 14.7%, an XYZ-Wing in 1.9%, and a naked or hidden triple, X-Wing or Swordfish in 1.6% between them. The other 76.0% need techniques this guide does not cover yet, almost all of them chains.
Cells are named by row and column: r4c1 is row 4, column 1. Rows count from the top, columns from the left, and boxes are numbered 1 to 9 reading like a book, so box 1 is top-left and box 9 is bottom-right.
Put them to work
Free Sudoku in your browser, at four difficulty levels.
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