Sudoku Strategies: From Beginner to Expert

Scanning is the first technique every solver should learn. Pick a digit (say, 5) and scan the grid box by box. For each 3×3 box that does not contain that digit, check which rows and columns passing through the box already have it.

By eliminating rows and columns, you narrow down where the digit can go within the box. When only one cell remains, that is where the digit belongs. Repeat for all nine digits across all nine boxes.

When a row, column, or box has only one empty cell, the missing digit is immediately obvious - it is the only digit from 1-9 not already present in that group.

This technique seems trivial, but it is surprisingly powerful. Each digit you place can create new last-remaining-cell situations elsewhere. Always re-scan after placing a digit to catch these chain reactions.

A naked single is a cell where all candidates except one have been eliminated by the digits in its row, column, and box. When you write pencil marks for a cell and only one candidate remains, that is a naked single - fill it in.

To find naked singles efficiently, maintain pencil marks for all empty cells. After placing each digit, immediately update the pencil marks in the affected row, column, and box. Naked singles will reveal themselves automatically.

A hidden single occurs when a digit can only go in one cell within a row, column, or box - even if that cell has multiple candidates. Unlike a naked single (where the cell has one candidate), a hidden single is about the digit having only one possible location in a group.

To find hidden singles, check each digit within each group. If the digit 3 can only go in one cell within row 5, then 3 must go there, regardless of what other candidates that cell has. Hidden singles are easily overlooked but incredibly powerful.

A naked pair occurs when two cells in the same row, column, or box have exactly the same two candidates - and only those two. For example, two cells in row 3 both contain only {4, 7}.

Since those two digits must go in those two cells (in some order), you can safely eliminate 4 and 7 from all other cells in that row. This often unlocks new naked or hidden singles elsewhere.

A naked triple works like a naked pair but with three cells. Find three cells in the same row, column, or box that together contain only three candidate digits. Each cell doesn't need all three candidates - for example, cells with {1,3}, {1,7}, and {3,7} form a naked triple for digits 1, 3, and 7.

Once identified, you can remove all three digits from every other cell in that unit. Naked triples are common in medium-to-hard puzzles and often appear after initial singles and pairs are placed.

A hidden pair exists when two digits appear as candidates in exactly two cells within a group - and nowhere else in that group. Even if those cells have other candidates, you know the two digits must go in those cells.

The power of hidden pairs is that you can eliminate all other candidates from those two cells, often revealing naked singles or enabling further eliminations. Hidden pairs require careful candidate tracking to spot.

When a candidate digit within a 3×3 box is confined to a single row or column, that digit can be eliminated from the rest of that row or column outside the box. The pair "points" along the line.

For example, if the digit 8 can only appear in the top row of box 1, then 8 cannot appear in the top row of boxes 2 or 3. This technique bridges the relationship between boxes and lines.

If a candidate digit within a 3×3 box is confined to a single row (or column), that digit cannot appear anywhere else in that row (or column) outside the box. The box effectively "claims" the digit for that line.

The reverse also works: if a candidate in a row is confined to one box, eliminate it from the rest of that box. This technique bridges box constraints and line constraints and often unlocks cells that other methods miss.

The X-Wing pattern occurs when a candidate digit appears in exactly two cells in each of two separate rows, and those cells line up in the same two columns - forming the corners of a rectangle.

When you find an X-Wing, the candidate must be in one pair of diagonally opposite corners. This means you can eliminate that candidate from all other cells in those two columns (or rows, if the pattern aligns by columns).

X-Wing is often the breakthrough technique that unlocks expert-level puzzles. Look for it when you have a candidate that appears exactly twice in two rows and those occurrences share columns.

Swordfish extends the X-Wing concept to three rows and three columns. A candidate digit appears in two or three cells in each of three rows, and these cells are confined to the same three columns.

The logic is the same as X-Wing but covers a larger area. You can eliminate the candidate from all other cells in the three involved columns. Swordfish patterns are harder to spot but devastatingly effective on evil puzzles.

An XY-Wing involves three cells, each containing exactly two candidates. A pivot cell with candidates {X, Y} sees one cell with {X, Z} and another cell with {Y, Z}. The two "wing" cells are not in the same row, column, or box as each other.

In this arrangement, Z must appear in at least one of the wing cells. Therefore, any cell that sees both wings cannot contain Z. This is a powerful elimination technique for breaking through stuck positions.

A forcing chain starts by assuming a candidate is either true or false in a particular cell, then following the logical implications in each direction. If both assumptions lead to the same conclusion about another cell, that conclusion must be true.

For example, if assuming digit 5 is in cell A leads to digit 3 being in cell B, and assuming digit 5 is NOT in cell A also leads to digit 3 being in cell B, then digit 3 must be in cell B regardless.