Master Sudoku with proven strategies from beginner to expert. Learn scanning, elimination, naked pairs, X-Wing, and more techniques to solve any puzzle.
Sudoku looks deceptively simple. A 9x9 grid, some numbers already filled in, and one rule: every row, column, and 3x3 box must contain the digits 1 through 9 exactly once. No math required. No trivia knowledge. Just logic.
Yet that simplicity hides extraordinary depth. Easy puzzles yield to basic scanning in minutes. Hard puzzles can stall experienced solvers for hours. And the difference between struggling and flowing through a puzzle almost always comes down to technique — knowing which strategy to apply and when.
Whether you are picking up your first puzzle or trying to crack the expert-level grids that have been haunting you, this guide covers every major Sudoku solving technique from the fundamentals to the advanced. Each strategy builds on the previous ones, so start from the beginning even if you consider yourself intermediate.
Ready to practice as you learn? Play Sudoku online and apply these techniques in real time.
Before diving into strategies, make sure the rules are crystal clear. Sudoku is played on a 9x9 grid divided into nine 3x3 boxes (also called blocks or regions). Some cells are pre-filled with digits — these are the "givens."
Your job is to fill every empty cell so that:
That is it. No addition, no multiplication, no guessing. Pure logical deduction. Every valid Sudoku puzzle has exactly one solution.
These techniques will solve most easy and many medium puzzles. Master them before moving on.
Scanning is the most natural technique. You look at a row, column, or box and ask: "What numbers are missing?" Then you check whether any of those missing numbers can only go in one place.
There are two types of scanning:
Cross-hatching — Pick a number, say 7. Look at a 3x3 box where 7 is missing. Check the rows and columns that pass through that box. If 7 already appears in some of those rows and columns, it eliminates certain cells. If only one cell remains, that is where 7 goes.
Imagine a 3x3 box with six empty cells. The number 5 is missing from this box. You check the three rows passing through the box — 5 already appears in two of them. You check the three columns — 5 already appears in two of them. The intersection of the one remaining row and one remaining column gives you exactly one cell. That is where 5 must go.
Counting — Look at a row, column, or box and list all missing numbers. If a cell can only hold one of those missing numbers (because the others are eliminated by its row, column, or box), you have found your answer.
Scanning is fast, effective, and should be your first pass on every puzzle. Go through each number 1 through 9 and scan for easy placements.
A hidden single occurs when a number can only go in one cell within a row, column, or box — even though that cell might have other candidates too.
For example, in a particular row, the number 3 is missing. You check each empty cell in that row. Most of them already have a 3 in their column or box, eliminating them. Only one empty cell in the row can accept a 3. That cell must be 3, regardless of what other numbers could also fit there.
Hidden singles are essentially what you find through scanning, but thinking of them as a named technique helps you be systematic. Check every row, every column, and every box for each number.
A naked single is even simpler conceptually: a cell where only one candidate is possible. After checking the cell's row, column, and box, you have eliminated eight of the nine digits. The remaining digit is the answer.
Finding naked singles requires you to track candidates — the list of possible numbers for each cell. Many solvers write small "pencil marks" in the corners of cells. This bookkeeping pays off enormously as puzzles get harder.
When scanning and singles stop producing results, these techniques will get you moving again. They work by eliminating candidates rather than directly placing numbers.
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 a row both have candidates 7 and nothing else.
You do not know which cell is 4 and which is 7, but you know for certain that those two cells account for both 4 and 7 in that row. Therefore, you can eliminate 4 and 7 from every other cell in that row.
Picture a row where cell A has candidates 7 and cell B also has candidates 7. Cell C has candidates 9. Because 4 is locked into cells A and B, you can remove 4 from cell C, leaving it with 9. This might create a naked single or enable another technique.
The same logic extends to three cells. If three cells in a row, column, or box have candidates drawn exclusively from three numbers, those three numbers are locked into those three cells. Remove them from all other cells in that unit.
An important subtlety: each cell does not need all three candidates. For instance, cells with 5, 8, and 8 form a naked triple on 8. The key is that the union of their candidates contains exactly three numbers, and there are exactly three cells.
Where naked pairs involve cells that contain only the paired candidates, hidden pairs involve candidates that appear in only two cells within a unit — but those cells might have other candidates too.
If the numbers 3 and 6 appear as candidates in only two cells within a box, then those two cells must contain 3 and 6. You can eliminate all other candidates from those two cells.
Hidden triples follow the same pattern: three numbers that appear in only three cells within a unit.
Sometimes the interaction between a box and a line (row or column) yields eliminations.
Pointing pairs — If a candidate number within a 3x3 box is restricted to a single row (or column), then that number must appear in that row within that box. You can eliminate that candidate from the same row in the other two boxes it passes through.
For example, within a box, the number 9 can only go in two cells, and both cells are in the same row. Since 9 must be in that row within this box, it cannot be in that row in any other box. Eliminate 9 from that row outside the box.
Box-line reduction — The reverse. If a candidate in a row is restricted to a single box, eliminate it from the rest of that box.
These techniques exploit the dual membership every cell has — it belongs to both a box and a line. When constraints in one unit force a number into a specific region, the other unit benefits.
These strategies are rarely needed for medium puzzles but become essential for hard and expert grids. They require careful candidate tracking and spatial reasoning.
The X-Wing pattern involves a single candidate number and exactly two rows (or columns). If a candidate appears in exactly two cells in each of two rows, and those cells align in the same two columns, then that candidate must occupy the corners of the rectangle formed by those rows and columns.
Visualize it: rows 2 and 7 each have the candidate 5 in exactly two cells. Those cells happen to fall in columns 3 and 8. This creates four cells forming a rectangle. The number 5 must appear in two of those four cells — specifically, in one diagonal pair. This means 5 cannot appear anywhere else in columns 3 and 8. Eliminate 5 from all other cells in those two columns.
The X-Wing works because of a simple constraint: if 5 is in row 2, column 3, then 5 in row 7 must be in column 8 (and vice versa). Either way, columns 3 and 8 are covered.
Swordfish is the X-Wing's bigger sibling. Instead of two rows and two columns, it involves three rows and three columns.
If a candidate appears in two or three cells in each of three rows, and all those cells fall within the same three columns, the candidate can be eliminated from all other cells in those three columns.
The logic is identical to the X-Wing, just scaled up. The candidate must fill exactly three of the cells at the intersections, one per row and one per column. Every other occurrence of that candidate in those three columns is impossible.
Swordfish patterns are harder to spot because the cells do not always form a neat rectangle — they form a more scattered pattern across the three-by-three grid of intersections. Systematic candidate tracking makes them findable.
Coloring is a technique based on cells that form conjugate pairs — two cells in a unit that are the only two places a candidate can go.
Start with any candidate, say 6. Find a cell where 6 is one of two positions in its row. Color that cell blue and the other cell green. Now look at the green cell — is 6 also a conjugate pair in its column or box? If so, the other cell in that pair gets blue. Continue the chain, alternating colors.
The key insight: all blue cells or all green cells contain the number 6. This leads to two types of elimination:
Color trap — If an uncolored cell can "see" (shares a row, column, or box with) both a blue cell and a green cell, it cannot contain 6. One of those colored cells definitely has 6, so the uncolored cell is eliminated.
Color wrap — If two cells of the same color can see each other, that color is impossible. All cells of that color are eliminated, and the other color is correct.
Bifurcation (also called backtracking or trial and error) means picking a cell with two candidates, assuming one is correct, and following the logic to see if it leads to a contradiction. If it does, the other candidate must be correct.
Most Sudoku purists consider bifurcation inelegant because it replaces deduction with hypothesis testing. Every well-constructed Sudoku puzzle is solvable without it. However, knowing it exists is useful for two reasons: it guarantees you can always make progress, and sometimes what looks like bifurcation is actually an advanced deduction technique you have not learned yet.
If you find yourself needing bifurcation frequently, it usually means there is a technique in your arsenal that needs sharpening. Go back and look for patterns you might have missed.
Beyond specific techniques, these habits will improve your solving speed and accuracy.
Always pencil mark systematically. In harder puzzles, trying to hold all candidates in your head leads to mistakes. Write them down. Update them after every placement. The bookkeeping is what makes advanced techniques possible.
Work through numbers in order. When scanning, go 1 through 9 systematically. This prevents you from fixating on one area and missing easy placements elsewhere.
Focus on the most constrained areas. A box with seven filled cells only has two unknowns — start there. A row missing just two numbers is almost solved. Constraints are your friend; they narrow possibilities.
Look for intersections. The most powerful deductions happen where a row, column, and box overlap. A cell at the intersection of a nearly complete row, a nearly complete column, and a nearly complete box is heavily constrained.
Take breaks. If you are stuck, step away. Fresh eyes catch patterns that fatigued eyes miss. This is not a weakness — it is how human pattern recognition works.
Practice different difficulty levels. Do not only solve easy puzzles; you will plateau. Do not only attempt expert puzzles; you will get frustrated. Mix difficulties and you will steadily expand your technique range.
Even experienced solvers fall into these traps:
Sudoku is a skill, and like any skill, it improves with deliberate practice. Start with scanning and singles. Once those are automatic, add naked pairs to your toolkit. Then hidden pairs, pointing pairs, X-Wings. Each technique you internalize makes the next one easier to learn because you start to see the logical structures they share.
The beauty of Sudoku is that it rewards patience and precision. There is no luck involved, no hidden information, no opponent making unpredictable moves. Every puzzle is a conversation between you and pure logic. The better your vocabulary of techniques, the richer that conversation becomes.
If you enjoy the logical satisfaction of Sudoku, you might also love other puzzle games that exercise similar muscles. Play Minesweeper for probability-based deduction, try Nonogram for grid-based logic with a visual payoff, or challenge yourself with 2048 for a different flavor of strategic thinking.
Ready to put these strategies into practice? Play Sudoku right now and see how far your new techniques take you. Start with an easy puzzle to warm up your scanning, then push into hard territory and watch as naked pairs and X-Wings reveal themselves. Every puzzle you solve makes you sharper for the next one.
Akousa