Strategy Guide

Sudoku Strategies & Solving Techniques

A complete reference of Sudoku solving methods — from the simplest single candidate scan to advanced patterns like X-Wing and Swordfish. Each technique is explained with clear logic, concrete grid coordinates, and concise examples. Start by scanning rows, columns, and 3×3 boxes; build pencil marks for every empty cell; then progressively apply stronger techniques as the puzzle resists basic moves.

Naked Singles (Sole Candidate)Hidden Singles Naked Pairs & Triples Pointing Pairs & Box-Line Reduction X-Wing Swordfish XY-Wing

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The simplest and most fundamental technique. If a cell can only contain one possible number, that is the answer.

Look at every empty cell and check which numbers 1–9 are already present in its row, column, and 3×3 box.
If eight different numbers are already ruled out, the remaining digit is the only possible candidate.
Always scan the board after every placement — one solved cell often unlocks several others.
This technique alone is sufficient to solve Easy-level puzzles.

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Imagine a cell in row 3, column 5. Row 3 contains 1, 4, 6, 9; column 5 contains 2, 5, 7; and the box contains 3, 8. Only 2 is missing, so that cell must be 2.

A number can only go in one cell inside a row, column, or box — even if that cell has other candidates.

Scan a single row and look at where digit '5' could legally go. If there is only one empty cell in that row that doesn't already see a 5 in its column or box, that cell must be 5.
This is called 'hidden' because the cell may have multiple pencil-mark candidates, but the 5 is forced by the house constraint.
Apply this to every digit 1–9 across every row, column, and box.
Hidden Singles are the workhorse of Medium puzzles and often appear after a few Naked Singles.

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In a 3×3 box, cells are empty except for the center cell which can be 2, 5, or 8. Every other empty cell in that box is blocked from being a 2 by row/column conflicts. Therefore the center cell must be 2.

If two cells in the same house contain an identical pair of candidates, those two numbers are locked to those cells and can be eliminated elsewhere in the house.

Identify two cells in a row (or column, or box) that both have exactly the same two candidates, e.g., {3, 7}.
Even if you don't know which is 3 and which is 7, you know those two numbers are committed to those two cells.
Therefore, remove 3 and 7 from all other candidate lists in that same house.
Naked Triples work the same way: three cells with a total of three distinct candidates among them lock those digits.

// EXAMPLE

In a row, cells 2 and 7 both show candidates {4, 9}. No other cell in that row can be 4 or 9. If cell 5 had {4, 6, 8}, you can safely erase the 4, leaving {6, 8}.

When a candidate inside a box is restricted to one row or column, it cannot appear elsewhere in that same row or column outside the box.

Look at a 3×3 box. If candidate '6' appears only in the top row of that box, then the 6 for that entire top row must be inside this box.
This lets you eliminate candidate 6 from other cells in that top row that lie outside the box.
The reverse is also true: if a candidate appears only in one box along a row, eliminate it from other cells inside that box.
Pointing Pairs are especially powerful because they connect box logic with line logic.

// EXAMPLE

In the top-left box, the only places digit 2 can go are cells (1,1) and (1,2) — both in row 1. Therefore, no other cell in row 1 can contain a 2.

A candidate appears exactly twice in two rows, and those two occurrences line up in the same two columns — forming a rectangle that locks the digit.

Scan all rows for a candidate digit that appears exactly twice.
If two different rows both have that candidate in exactly the same two columns, you have found an X-Wing.
The four cells form the corners of a rectangle. The digit must occupy opposite corners, so it is locked to those two rows and two columns.
You can now eliminate that candidate from all other cells in those two columns (or rows, depending on orientation).
Look for the complementary pattern too: two columns with the same candidate in exactly two rows.

// EXAMPLE

Rows 2 and 7 both have candidate 5 only in columns 3 and 8. This X-Wing means column 3 and column 8 get their row-2 and row-7 5s from these rows, so no other row can place a 5 in columns 3 or 8.

An extension of X-Wing to three rows and three columns. A candidate is confined to three cells in each of three rows, and those cells share only three columns.

Search for a candidate that appears at most three times in each of three different rows.
All those occurrences must fall within the same three columns.
This creates a 3×3 'net' where the candidate is locked. You can eliminate it from other cells in those three columns.
Swordfish can be difficult to spot visually. Many solvers scan one candidate at a time using pencil marks.
Jellyfish (4×4) follows the same logic but is rare in standard 9×9 puzzles.

// EXAMPLE

Candidate 3 appears in rows 1, 4, and 8 only within columns 2, 5, and 9. The Swordfish pattern guarantees that columns 2, 5, and 9 receive their 3s from these three rows, so other rows cannot place a 3 in those columns.

A chain of three bi-value cells forms a forcing pattern. The pivot cell (XY) sees two wing cells (XZ and YZ), forcing Z into any cell that sees both wings.

Find a pivot cell with exactly two candidates, e.g., XY.
Find two other cells that each see the pivot (share a row, column, or box) and have exactly two candidates: XZ and YZ.
The two wing cells (XZ and YZ) must not see each other directly.
If the pivot is X, then the XZ wing becomes Z. If the pivot is Y, then the YZ wing becomes Z. Either way, Z is forced.
Therefore, any cell that sees both wings can never be Z. Eliminate Z from those common peers.

// EXAMPLE

Pivot at (4,4) has {2,7}. Wing A at (4,1) has {2,9}. Wing B at (7,4) has {7,9}. Both wings see the pivot. Any cell that sees both (4,1) and (7,4) cannot be 9.

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Scanning

Always scan rows, columns, and boxes after every single placement. One digit often triggers a cascade of Naked and Hidden Singles across the board.

Pencil Marks

On paper or in your mind, keep candidate lists. Advanced techniques depend on seeing where candidates line up across multiple houses.

Pattern Memory

X-Wing and Swordfish are easier to spot if you mentally highlight one candidate at a time. Look for aligned pairs or triplets in rows and columns.