Sudoku Solver

Solving tactics

Naked single

A cell has only one possible value after eliminating numbers already present in its row, column, and 3×3 box. That value must be placed.

Hidden single

In a row, column, or 3×3 box, a candidate appears in only one cell’s candidate list. That cell must take the candidate even if it has other options.

Naked pair / triple / quad

In a row, column, or box, if exactly N cells contain the same N candidates, those candidates can be removed from all other cells in the unit.

Hidden pair / triple / quad

In a unit, if N candidates appear only in the same N cells, those cells must contain those candidates and all other candidates can be removed from them.

Pointing pair / triple

If a candidate in a 3×3 box is confined to one row or column, that candidate can be removed from the rest of that row or column outside the box.

Claiming pair / triple

If a candidate in a row or column is confined to a single 3×3 box, that candidate can be removed from the other cells of that box.

X-Wing

A candidate appears in exactly two cells in two rows (or columns), aligned to the same columns (or rows). Remove that candidate from other cells in those columns (or rows).

Swordfish

A candidate appears in 2–3 cells across three rows (or columns), aligned to the same three columns (or rows). Remove the candidate from other cells in those columns (or rows).

Jellyfish

A candidate appears in 2–4 cells across four rows (or columns), aligned to the same four columns (or rows). Remove the candidate from other cells in those columns (or rows).

XY-Wing

A pivot with candidates {X,Y} sees two wings {X,Z} and {Y,Z}. Any cell that sees both wings cannot contain Z.

XYZ-Wing

A pivot with {X,Y,Z} sees two wings {X,Z} and {Y,Z}. Any cell that sees the pivot and both wings cannot contain Z.

W-Wing

Two bivalue cells share {X,Y} and are linked by a strong link on X. Any cell that sees both cannot contain Y.

Skyscraper

A candidate appears twice in two rows (or columns), sharing one column (or row). Cells that see both “roof” positions cannot contain the candidate.