Sudoku techniques

from naked singles to forcing chains

Sudoku techniques

The sixteen techniques the step-by-step Sudoku Solver uses, from the two every player needs to the patterns that crack the hardest puzzles. A unit is a row, column or box; candidates are the digits still possible in a cell.

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Basic techniques

Naked Single: A cell where only one digit is still possible — every other digit already appears in its row, column or box. Place it.
Hidden Single: A digit that can go in only one cell of a row, column or box, even though that cell has other candidates. Place it there.

Intermediate techniques

Naked Pair: Two cells in one unit whose only candidates are the same two digits. Those digits must go in those cells, so remove them from every other cell in the unit.
Naked Triple: Three cells in a unit whose candidates, together, are just three digits. Remove those digits from the rest of the unit.
Hidden Pair: Two digits that can only go in the same two cells of a unit. Those cells hold those digits — remove every other candidate from them.
Pointing Pair: Inside a box, a digit's candidates all lie in one row (or column). The digit must be in that box's part of the line, so remove it from the rest of the line.

Advanced techniques

X-Wing: In two rows, a digit can only go in the same two columns. Whichever way round it goes, it fills both columns there — remove it from those columns in every other row.
Swordfish: The X-Wing idea across three rows and three columns.
XY-Wing: A pivot cell with candidates XY sees two wings, XZ and YZ. Whatever the pivot is, one wing is Z — so remove Z from any cell that sees both wings.
XYZ-Wing: Like an XY-Wing, but the pivot also holds Z (XYZ). Z can be removed from cells that see all three.
W-Wing: Two cells with the same pair XY, linked by a strong link on X. One of them must be Y, so Y is removed from cells that see both.
Unique Rectangle: Four cells in two rows, two columns and two boxes cannot all be limited to the same pair — that would give two solutions. The pattern forces the extra candidate in one corner.
BUG+1: If every unsolved cell had two candidates except one cell with three, the puzzle would have several solutions — so that cell takes the digit that breaks the pattern.

Last resorts techniques

Nishio: Assume one candidate and follow the consequences; if they lead to a contradiction, that candidate is removed.
Forcing Chains: Follow two or more chains of 'if this, then that' from one cell; whatever they agree on must be true.

Questions

Which Sudoku technique should I learn first?

Hidden singles. Scanning each box for the one place a digit can go solves most easy puzzles.

Do I need X-Wings to solve Sudoku?

Only for hard puzzles. Easy and medium puzzles need singles, pairs and pointing pairs at most.

Can I see these techniques on a real puzzle?

Yes — enter any puzzle in the step-by-step Sudoku Solver; it names and highlights each technique as it uses it.

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