Sudoku Strategies: From Basic to Advanced

Every technique you need, explained in plain language.

Basic Strategies

Naked Singles

Look at an empty cell. Check its row, column, and 3x3 box. Cross off every digit that already appears in any of those three groups. If only one digit remains, that is the answer. This is the most common move in Sudoku and the only technique you need for easy puzzles.

Hidden Singles

Sometimes a cell has multiple candidates, but one of those candidates cannot go anywhere else in the same row, column, or box. That candidate must go in this cell. For example, if the number 3 can only fit in one cell within a 3x3 box, it must go there, no matter what other candidates that cell has.

Scanning (Cross-Hatching)

Pick a number, say 5. Look at each 3x3 box and find where 5 already appears. For boxes that do not have a 5, draw imaginary lines through the rows and columns that already contain a 5. The remaining empty cells in that box are the only places 5 can go. If only one cell is left, fill it in.

Intermediate Strategies

Pencil Marks (Candidates)

Write small numbers in each empty cell to show which digits are still possible. As you solve cells, erase candidates from related cells. Good pencil marks make all advanced techniques work. Many solvers skip this step and get stuck. Do not skip it.

Naked Pairs

If two cells in the same row, column, or box each have the same two candidates (and only those two), then those two numbers must go in those two cells. You can remove both numbers from all other cells in that group. For example, if cells A and B in a row both have candidates {2, 7}, no other cell in that row can be 2 or 7.

Hidden Pairs

If two candidates appear in exactly two cells within a group, those two cells must hold those two numbers. You can remove all other candidates from those two cells. The pair is “hidden” because the cells may have other candidates that obscure it.

Naked Triples

Three cells in a group that together contain exactly three candidates. The three numbers must go in those three cells, so remove them from all other cells in the group. Each cell does not need all three candidates. For example, cells with {1, 3}, {1, 7}, and {3, 7} form a naked triple.

Pointing Pairs

If a candidate appears in only one row (or column) within a 3x3 box, that candidate can be removed from the rest of that row (or column) outside the box. The logic: the number must go in this box, and it must be in this row, so it cannot also be in this row in another box.

Box-Line Reduction

The opposite of pointing pairs. If a candidate in a row or column is restricted to a single box, you can remove that candidate from all other cells in that box. The number must go somewhere in this row-within-the-box, so no other cell in the box can have it.

Advanced Strategies

X-Wing

Find a candidate that appears in exactly two cells in each of two different rows, and those cells line up in the same two columns. The candidate must go in two of those four cells (forming a rectangle). You can remove that candidate from all other cells in those two columns. This is one of the most powerful techniques and the first real “advanced” move most solvers learn.

Swordfish

An extension of X-wing using three rows and three columns instead of two. A candidate appears in two or three cells per row, and all those cells fall within the same three columns. The candidate can be removed from all other cells in those three columns. Swordfish patterns are harder to spot but follow the same logic as X-wing.

XY-Wing

A pivot cell with two candidates connects to two wing cells, each sharing one candidate with the pivot and having one unique candidate. Any cell that sees both wing cells can have the shared extra candidate removed. This technique solves cells that no other method can reach in some puzzles.

Coloring (Simple Colors)

Pick a candidate and trace its possible positions through the grid using chains. Color alternating positions with two colors. If two cells with the same color can see each other, that color is false and the other is true. This eliminates candidates and reveals solutions in complex puzzles.

When to Use Each Strategy

• Easy puzzles: Naked singles and hidden singles are enough.
• Medium puzzles: Add pencil marks, naked pairs, and pointing pairs.
• Hard puzzles: Use hidden pairs, triples, and box-line reduction.
• Expert puzzles: You will need X-wing, swordfish, XY-wing, and coloring.

Practice each technique one at a time. Solve puzzles that require it, then move on. Our puzzle books are organized by difficulty so you can build skills in the right order.