Sudoku Rules & Techniques
Sudoku is a puzzle game with very simple rules. It uses numbers but involves no math, only logical deduction.
Basic Rules of Sudoku
- The grid is 9 by 9 cells, divided into nine 3 by 3 boxes.
- Some cells are filled in at the start. These are your starting clues.
- Your job is to fill in the empty cells.
- Each row must contain every digit from 1 to 9, with no repeats.
- Each column must contain every digit from 1 to 9, with no repeats.
- Each 3 by 3 box must contain every digit from 1 to 9, with no repeats.
- You win when every cell is filled in correctly.
Basics
Every Sudoku puzzle is a closed system of logical constraints. The techniques below are the precise deduction patterns that flow from the rules of the game.
Last Free Cell
When only one empty cell remains in a row, column, or box, it must contain the one digit that's missing from that region.Last Remaining Cell
When a digit can’t fit in any cell within a region except one, the one cell left unblocked is the only valid placement.Last Possible Number
When a cell's row, column, and box together contain all digits but one, that remaining digit is the only valid entry.Notes in Sudoku
Pencil marks let you record which digits are still possible in each empty cell. Tracking these candidate digits is required to apply intermediate and advanced techniques.Bread & Butter
Using notes, you can compare candidates across multiple cells within a region, or track how a digit's possible positions in one region affect another.
Obvious Singles
A cell where every digit except one has been eliminated by the constraints of its row, column, and box. That remaining digit is the answer.Obvious Pairs
Two cells in the same region that share exactly the same two candidates. Those two digits can be removed from all other cells in that region.Obvious Triples
Three cells in a region that together contain only three candidates. Those digits can be eliminated from every other cell in that region.Hidden Singles
A digit that appears as a candidate in only one cell within a region, even though that cell has other candidates. That cell must hold that digit.Hidden Pairs
Two digits that only appear in the same two cells within a region. All other candidates in those two cells can be removed.Hidden Triples
Three digits confined to the same three cells in a region. Any other candidates in those three cells can be safely eliminated.Pointing Pairs
When a digit's only candidates within a box all fall in the same row or column, that digit can be eliminated from the rest of that row or column outside the box.Pointing Triples
The same logic as pointing pairs, but with three candidates aligned in a box. The digit is eliminated from the rest of that row or column.Advanced
To eliminate candidates at scale, you can identify patterns that span multiple rows and columns at once.