Sudoku solving techniques
Every Sudoku can be solved with a small set of logical techniques. This index lists the nine techniques that the Bare Sudoku solver and its hints use, in the order the solver tries them: singles first, then eliminations within one unit, then patterns that span several rows and columns. Each technique has its own page with a definition, how to spot it, a real example from a generated puzzle and the common mistakes.
The level of a puzzle is decided by the hardest technique it needs. Easy and Medium puzzles need only singles, Hard puzzles need locked candidates or pairs and triples, and Expert puzzles need at least one fish or wing. Whatever the level, singles do most of the work; the advanced technique removes a candidate or two and singles carry on from there.
Cells are written as r3c7: row 3, column 7. Rows are counted from the top, columns from the left, and boxes 1 to 9 from the top left, row by row.
- Naked singleEasy
A naked single is an empty cell with only one possible digit. Learn how to find naked singles quickly, with a real example step by step and the usual mistakes. - Hidden singleEasy
A hidden single is the only cell in a row, column or box where a digit can still go. Learn to spot hidden singles by scanning one digit at a time. - Locked candidatesHard
Locked candidates: when a digit's candidates in a box all lie in one row or column, or the reverse, the digit is removed elsewhere. Two real examples. - Naked pairs and triplesHard
Naked pairs and triples: two or three cells in a unit that share the same two or three candidates. Learn to spot them and what to remove, with real examples. - Hidden pairs and triplesHard
A hidden pair is two digits that can only go in the same two cells of a unit, so their other candidates go. Learn to find hidden pairs and triples step by step. - X-WingExpert
X-Wing: a digit with exactly two candidate cells in two rows, lined up in the same two columns, is removed from the rest of those columns. Real example. - Y-WingExpert
Y-Wing (XY-Wing): a pivot with two candidates and two wings that each share one of them force a digit out of every cell that sees both wings. Example. - SwordfishExpert
Swordfish: a digit confined to three columns across three rows is removed from the rest of those columns. The size-three fish, explained with a real example. - XYZ-WingExpert
XYZ-Wing: a pivot with three candidates and two wings that share one of them force that digit out of every cell seeing all three. Real example, step by step.
Frequently asked questions
In which order should I try Sudoku techniques?
Cheapest first: naked singles, hidden singles, locked candidates, naked pairs and triples, hidden pairs and triples, X-Wing, Y-Wing, Swordfish, XYZ-Wing. Bare Sudoku tries them in exactly this order, and a hint always names the simplest technique that makes progress.
Do I need all these techniques to solve Sudoku?
For Easy and Medium puzzles, singles are enough. Hard puzzles add locked candidates and subsets. Expert puzzles need at least one fish or wing, but usually only once or twice per puzzle.
Are there harder techniques than XYZ-Wing?
Yes, for example chains, uniqueness tests and forcing nets. Bare Sudoku does not generate puzzles that need them, so every puzzle in the game can be finished with the nine techniques on this page.
What is a candidate?
A digit that could still go in an empty cell because nothing in its row, column or box rules it out yet. Notes in the game are candidates. Every technique beyond singles reasons about candidates, so keep them complete and accurate.