How to Play Sudoku — Complete Beginner's Guide, Rules & Strategies

What Is Sudoku?

Sudoku is a number puzzle played on a 9×9 grid divided into nine 3×3 boxes. Fill every row, column, and box with the digits 1 through 9, no repeats. No math — just logic.

The concept traces back to 18th-century "Latin Squares." An American architect named Howard Garns turned it into a puzzle in 1979, and Japanese newspapers popularized it in the mid-1980s under the name Sudoku ("single number"). It's been a newspaper staple ever since, and now you can play it here.

The Rules (In 30 Seconds)

Sudoku has exactly three rules:

1. Each row must contain the digits 1–9 with no repeats.
2. Each column must contain the digits 1–9 with no repeats.
3. Each 3×3 box must contain the digits 1–9 with no repeats.

That's it. Every cell on the board has exactly one correct answer, and every well-formed Sudoku puzzle has exactly one solution. You never need to guess — if you're guessing, there's a deduction you're missing.

How to Start: Reading the Grid

When you open a puzzle, some cells are pre-filled (called givens). These are your anchors. A typical medium puzzle has 28–32 givens; a hard puzzle might have as few as 22.

Start by scanning the grid. Look at each row, column, and box to see which numbers are already placed. The more numbers you can see in a row/column/box, the fewer candidates remain for the empty cells — and the easier it is to narrow things down.

Pencil marks (also called candidates or notes) make everything easier. For each empty cell, jot down every digit that could go there based on the three rules. As you solve cells, erase those digits from neighbors' pencil marks. Every technique below builds on this habit.

Beginner Strategy: Naked Singles

A naked single is the simplest Sudoku technique. If a cell's pencil marks have been reduced to just one digit, that digit is the answer. Place it and remove it from the pencil marks of every cell in the same row, column, and box.

Example: if a cell in row 3 can only contain a 7 (because 1–6 and 8–9 all appear elsewhere in its row, column, or box), then it must be 7. This is the most common solving move and will carry you through most easy puzzles.

Beginner Strategy: Hidden Singles

A hidden single occurs when a digit can only go in one place within a row, column, or box — even though that cell might have multiple candidates.

Example: suppose in Box 5, the digit 4 only appears as a candidate in one cell. Even if that cell also has 4, 6, and 9 as candidates, you know it must be 4 because no other cell in that box can hold a 4. Place it.

Scanning for hidden singles box by box is the fastest way to make progress on medium-difficulty puzzles.

Intermediate Strategy: Pointing Pairs & Box/Line Reduction

Once naked and hidden singles dry up, look for pointing pairs. If a candidate digit appears in a box but only in one row (or one column), then that digit can be eliminated from that row (or column) outside the box.

The reverse is box/line reduction: if a digit in a row or column is confined to a single box, eliminate it from the rest of that box.

These techniques don't place a number directly, but they reduce pencil marks — which often reveals new naked or hidden singles.

Advanced Strategy: Naked Pairs & Triples

A naked pair is when two cells in the same row, column, or box share exactly the same two candidates (e.g., both contain only {3, 7}). Since those two digits must go in those two cells, you can remove 3 and 7 from every other cell in that group.

Naked triples work the same way with three cells and three candidates. The cells don't each need all three digits — they just need to collectively contain only three distinct candidates.

The mirror technique is hidden pairs/triples: if two digits only appear as candidates in the same two cells within a group, those cells can only contain those two digits — eliminate all other candidates from them. Hidden pairs are harder to spot but equally powerful.

Advanced Strategy: X-Wing

The X-Wing is your first "fish" pattern and one of the most satisfying techniques to spot. It works on a single candidate digit across two rows (or two columns).

Here's the setup: pick a candidate digit (say, 5). Find two rows where 5 appears as a candidate in exactly two cells each — and those cells line up in the same two columns. These four cells form a rectangle. Because of the Sudoku rules, the 5 must go in one diagonal pair or the other. Either way, no other cell in those two columns can contain a 5.

How to apply it:

1. Pick a digit and scan rows (or columns) for exactly two candidate positions.
2. Look for another row with candidates in the same two columns.
3. Eliminate that digit from all other cells in those two columns.

Example: if row 2 has candidate 5 in columns 3 and 7, and row 8 also has candidate 5 in columns 3 and 7, you can remove 5 from every other cell in columns 3 and 7. The logic also works the other way — start from columns and eliminate from rows.

Advanced Strategy: Swordfish

The Swordfish extends X-Wing from 2 rows to 3. It's a 3×3 fish pattern, harder to spot but devastatingly effective.

Pick a candidate digit. Find three rows where that digit appears in only two or three cells each, and all those cells fall within the same three columns. The digit must be placed once per row within those columns, which means it can be eliminated from all other cells in those three columns.

The key insight: the candidate positions don't need to form a perfect 3×3 rectangle. Some intersections can be empty. What matters is that each row's candidates are confined to the same set of three columns.

Spotting tip: if X-Wings aren't producing eliminations, look for rows with 2-3 candidates for the same digit and check whether three of them share columns. It's rare but game-changing when it appears.

Beyond Swordfish, the pattern continues to Jellyfish (4 rows × 4 columns), but these are extremely rare in standard puzzles and most solvers never need them.

Advanced Strategy: XY-Wing

The XY-Wing (also called Y-Wing) is an advanced elimination technique that uses three cells with two candidates each.

You need a pivot cell with candidates {X, Y} and two wing cells that each see the pivot:

• Wing 1 has candidates {X, Z} and sees the pivot.
• Wing 2 has candidates {Y, Z} and sees the pivot.

The pivot must contain X or Y. If it's X, Wing 1 becomes Z. If it's Y, Wing 2 becomes Z. Either way, one of the wings must be Z. So any cell that sees both wings can have Z eliminated.

How to find them:

1. Look for cells with exactly two candidates (bi-value cells).
2. Pick one as a pivot and check if two of its peers also have two candidates that share one digit each with the pivot and one digit with each other.
3. The shared digit between the wings (Z) can be eliminated from cells that see both wings.

XY-Wings are the gateway to understanding chains — they're essentially the simplest form of a forcing chain.

Expert Strategy: Simple Coloring

Simple Coloring (also called single-digit coloring) uses the logical structure of conjugate pairs — pairs of cells in a group where a digit can only go in one of two places.

Pick a digit and find all conjugate pairs for it. Connect them into a chain, alternating two "colors" (think of them as ON and OFF). If a digit is in cell A or cell B (conjugate pair), color A green and B blue. If B is conjugate with C in another group, color C green (opposite of B). Continue building the chain.

Two rules produce eliminations:

1. Color trap: If an uncolored cell sees both a green and a blue cell, that digit can be eliminated from the uncolored cell — because one of the two colors must be "on."
2. Color wrap: If two cells of the same color can see each other (they share a row, column, or box), that color is impossible — the other color is entirely correct. Place the digit in all cells of the surviving color.

Simple coloring is powerful because a single chain can produce many eliminations at once. It's also intuitive once you start thinking in terms of "if this cell is X, then that cell isn't, then that cell is…"

Expert Strategy: Forcing Chains & AICs

Forcing chains are the most powerful general-purpose solving technique. The idea: assume a candidate is true (or false) in a cell and follow the logical consequences. If the chain reaches a contradiction, your assumption was wrong. If two different starting assumptions both lead to the same conclusion, that conclusion must be true.

There are several types:

• Contradiction chain: Assume candidate X in cell A. Follow the implications through linked cells. If you reach an impossible state (e.g., a cell with no candidates, or a group with no place for a digit), then X cannot go in cell A.
• Verity chain (double implication): Try both candidates in a bi-value cell. If both paths force the same digit into the same cell, that digit is confirmed regardless of which assumption is true.
• Alternating Inference Chain (AIC): A more structured form. Build a chain of strong and weak links between candidates. Strong link: exactly one of two must be true. Weak link: at most one can be true. If a chain starts and ends on the same digit with strong links at both ends, cells that see both endpoints can have that digit eliminated.

When to use chains: Only when all "pattern" techniques (X-Wing, XY-Wing, coloring) fail. Chains are powerful but slow and mentally taxing. Most newspaper-grade puzzles never require them, but competition puzzles and extreme-rated puzzles often do.

Building chain intuition: Start small. Practice with short chains (3-4 links) and work up. The key skill is seeing connections — how placing or removing a digit in one cell forces consequences elsewhere. Over time, you'll start spotting chain opportunities without consciously looking for them.

Expert Strategy: Hidden & Naked Quads

Naked quads extend the pairs/triples concept to four cells. If four cells in a group collectively contain only four distinct candidates, those digits can be eliminated from all other cells in that group.

Like naked triples, each cell doesn't need all four digits — the four cells just need to share no more than four distinct candidates between them. For example, cells with {1,2}, {2,3}, {3,4}, and {1,4} form a naked quad on digits 1-2-3-4.

Hidden quads are the reverse: if four digits appear only in four cells within a group, those cells can have all other candidates removed. Hidden quads are notoriously hard to spot — most solvers find them by elimination after trying everything else.

In practice: quads are rare and usually appear in expert-level puzzles. If you're stuck and you've checked for X-Wings and coloring, scan for quads before moving to chains.

The Solving Hierarchy

Experienced solvers work through techniques in a consistent order, from cheapest to most expensive:

1. Naked singles — scan the whole grid
2. Hidden singles — scan by box, then row, then column
3. Pointing pairs / box-line reduction
4. Naked pairs/triples
5. Hidden pairs/triples
6. X-Wing
7. Simple coloring
8. XY-Wing
9. Swordfish
10. Naked/hidden quads
11. Forcing chains / AICs

After each elimination, go back to step 1. An advanced technique often unlocks a cascade of simple ones. The biggest mistake intermediates make is staying at the advanced level instead of re-scanning for basics after every move.

You don't need to master all of these to enjoy Sudoku. Techniques 1-4 will solve 90% of published puzzles. Techniques 5-8 cover another 8%. Only the most extreme puzzles demand the full toolkit.

Tips for Faster Solving

• Work systematically: Scan rows, then columns, then boxes. Don't jump around randomly.
• Use pencil marks early: Don't try to hold everything in your head. Good notation is the difference between a 5-minute solve and a 20-minute one.
• Look for the most-constrained areas: Rows, columns, or boxes with the fewest empty cells are the easiest to crack. Start there.
• Don't guess: Every placement should follow logically from the rules. If you feel stuck, you're missing a deduction — zoom out and scan again.
• Practice daily: Pattern recognition beats brute force, and the only way to build it is reps. Our Daily Sudoku helps.

Common Mistakes to Avoid

• Forgetting a constraint: The most common error is checking the row and column but forgetting the 3×3 box (or vice versa). Always check all three.
• Pencil mark errors: If you forget to erase a candidate after placing a number, your subsequent logic will be wrong. Stay disciplined about updates.
• Tunnel vision: Don't stare at one area for too long. If you're stuck, move to a different part of the grid — a solve elsewhere often unlocks your stuck area.

Difficulty Levels Explained

Sudoku difficulty isn't about the grid size — it's about which techniques you need:

• Easy: Solvable with naked and hidden singles alone. Great for warming up.
• Medium: Requires pointing pairs, box/line reduction, and occasionally naked pairs.
• Hard: Demands advanced techniques like naked triples, X-Wings, and chains. Often has fewer givens (22–26).
• Expert: Requires multiple advanced techniques chained together. You'll know when you're ready.

Our Sudoku starts at medium difficulty. If you're new, focus on mastering naked and hidden singles before tackling harder puzzles.