Sudoku Solving Techniques

Naked single Easy

When a cell has only one possible number — because all other numbers 1–9 already appear in its row, column, or box — that number is the answer. This is the most common technique and the first one to learn.

How to spot it: Look for cells where every number except one is already placed in the same row, column, or box.

Hidden single Easy

When a number can only appear in one cell within a row, column, or box — even if that cell has multiple possible candidates — it must go there.

How to spot it: Scan each row, column, and box for a number that fits in only one empty cell.

Naked pair Medium

When exactly two cells in the same row, column, or box contain only the same two candidates, those candidates can be eliminated from all other cells in that unit. The two numbers must go in those two cells — you just don't know which order yet.

Hidden pair Medium

When two numbers can only appear in the same two cells within a unit, all other candidates in those two cells can be eliminated — even though those cells may have more than two candidates.

Naked triple Medium

An extension of naked pair to three cells. When three cells in a unit collectively contain only three candidates (in any combination), those candidates can be removed from all other cells in that unit.

Pointing pairs / triples Medium

When a candidate in a box is restricted to one row or column, it can be removed from that row or column outside the box. The candidate "points" out of the box.

Box-line reduction Medium

The reverse of pointing pairs. When a candidate in a row or column is restricted to one box, it can be removed from the rest of that box. Also called "box claiming".

X-Wing Hard

When a candidate appears in exactly two cells in each of two rows, and those cells share the same two columns, the candidate can be eliminated from the rest of those two columns. Equally valid for columns eliminating rows.

Swordfish Hard

The three-row (or three-column) version of X-Wing. When a candidate appears in at most three cells across three different rows, and those cells all fall in the same three columns, the candidate can be eliminated from those columns in all other rows.

XY-Wing Expert

Uses three cells — a pivot with two candidates [XY] and two pincers [XZ] and [YZ]. Any cell that sees both pincers cannot contain Z. A powerful technique that can break difficult puzzles.

Simple coloring (conjugate chains) Expert

For a candidate that forms conjugate pairs (two cells in a unit where the candidate can only go in one of two cells), color one candidate "on" (orange) and the other "off" (blue). Follow the chain. If two same-colored cells share a unit, that color must be "off" — the other color is correct.

Unique rectangle Expert

Exploits the rule that a valid puzzle must have exactly one solution. If four cells forming a rectangle spanning two boxes contain only the same two candidates, a deadly pattern would create two solutions — so one of the cells must have an additional candidate that resolves the ambiguity.