Every row, every column and every 3×3 box must hold the digits 1 to 9, once each. That one rule is all there is: the techniques below are the ways people use it to find the next digit without guessing.
Most solvers pencil in the candidates, the digits that could still go in each empty cell. Each technique then either places a digit or rules candidates out. Start at the top and work down the list as the puzzles get harder.
The techniques, easiest first
- Naked single Easy
An empty cell with only one digit left that can go in it.
- Hidden single Easy
A digit with only one place left in a row, column or box.
- Pointing Medium
In a box, a digit fits only along one line: it goes from the rest of that line.
- Box–line reduction Medium
In a row or column, a digit fits only inside one box: it goes from the rest of that box.
- Naked pair Hard
Two cells in a row, column or box with the same two candidates, and no others.
- Hidden pair Hard
Two digits that fit in only the same two cells of a row, column or box.
- Naked triple Hard
Three cells in a row, column or box that hold only the same three digits between them.
- Hidden triple Hard
Three digits that fit in only the same three cells of a row, column or box.
- Naked quad Hard
Four cells in a row, column or box that hold only the same four digits between them.
- X-wing Expert
A digit with two places in each of two rows, lined up in the same two columns.
- XY-wing Expert
Three two-candidate cells: whichever way the middle one goes, one of the outer two is the same digit.
- XYZ-wing Expert
An XY-wing whose pivot also holds the shared digit: it goes from cells that see all three.
- Swordfish Expert
An X-wing over three rows: a digit’s places in three rows fall in the same three columns.
- X-chain Expert
One digit, followed from cell to cell: one end of the chain must hold it.
- XY-chain Evil
A chain of two-candidate cells: whichever way the first goes, one end is the same digit.
The hardest puzzles need still more: jellyfish and longer alternating chains. In the game, a hint names each technique as you meet it and shows it on your board.
