How do I play Sudoku online?

Simply click on any empty cell and select a number from 1-9. Use logic to determine which numbers can go in each cell based on Sudoku rules - each row, column, and 3x3 box must contain all numbers 1-9 exactly once.

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Can I compete with other players?

Yes! Take our daily challenges, track your solving times, and climb the global leaderboard. Compete with players worldwide and see how you rank against the best Sudoku solvers.

Are there different difficulty levels?

We offer 6 difficulty levels: Easy, Medium, Hard, Expert, Master, and Extreme. Each level provides the perfect challenge for your skill level, from beginners to world-class players.

Sudoku Rules: Complete Guide to Playing and Solving

Introduction

Sudoku is one of the world's most popular logic puzzles, and understanding its rules is the first step toward becoming a confident solver. This complete guide covers everything you need to know about Sudoku rules, from the three fundamental constraints that govern every puzzle to the techniques that help you solve them. Whether you're a complete beginner or looking to solidify your understanding, this guide provides a comprehensive foundation for mastering Sudoku.

The beauty of Sudoku lies in its simplicity: just three basic rules create puzzles of infinite variety and complexity. Once you understand these rules and how they work together, you'll be able to solve puzzles at any difficulty level. This guide will teach you not just what the rules are, but how to apply them effectively to solve puzzles systematically.

What Are Sudoku Rules?

Sudoku rules are the three fundamental constraints that every valid Sudoku puzzle must satisfy. These rules work together to create solvable puzzles that can be completed through pure logic without guessing. Understanding these rules is essential for solving any Sudoku puzzle, regardless of difficulty level.

The three rules are: (1) Each row must contain the digits 1-9 exactly once, (2) Each column must contain the digits 1-9 exactly once, and (3) Each 3×3 box must contain the digits 1-9 exactly once. These rules create a system of constraints where every number placement must satisfy all three rules simultaneously. This interaction between rules is what makes Sudoku puzzles solvable and challenging.

Sudoku rules are universal—they apply to all puzzles regardless of difficulty. Easy puzzles have more given numbers, making rule application simpler, while hard puzzles have fewer clues, requiring more sophisticated techniques, but the fundamental rules remain unchanged.

Key Points

Essential concepts for understanding Sudoku rules:

Three fundamental rules: Every number must be unique in its row, column, and 3×3 box—these constraints work together to create solvable puzzles
No repetition allowed: Each number 1-9 must appear exactly once in every row, every column, and every 3×3 box
Logic-based solving: Valid puzzles are always solvable through systematic reasoning using techniques like elimination and pattern recognition
No guessing required: Every valid Sudoku puzzle can be solved through pure logic—guessing is never necessary and often leads to errors
Progressive difficulty: Puzzles range from easy (many clues) to extremely difficult (few clues), but all follow the same three rules
Unique solution: Every valid puzzle has exactly one correct solution that satisfies all three rules

How It Works (Step-by-Step)

Follow this approach to understand and apply Sudoku rules:

Step 1: Understand the Grid Structure

A Sudoku grid consists of 81 cells arranged in 9 rows (horizontal) and 9 columns (vertical). The grid is also divided into 9 boxes, each containing 3×3 cells. Every cell belongs to exactly one row, one column, and one box. Understanding this structure is essential because each number you place must satisfy constraints in all three units.

Step 2: Learn the Three Rules

Every Sudoku puzzle follows three rules that work together. Rule 1: Each row must contain digits 1-9 exactly once. Rule 2: Each column must contain digits 1-9 exactly once. Rule 3: Each 3×3 box must contain digits 1-9 exactly once. Before placing any number, verify it doesn't violate any of these three rules.

Step 3: Start with Given Numbers

Examine the puzzle's given numbers (clues). These provide the starting information you'll use to deduce the remaining numbers. Easy puzzles have more given numbers (40-50), while hard puzzles have fewer (20-30). The fewer the clues, the more advanced techniques you'll need.

Step 4: Apply Rules Systematically

Use the three rules to eliminate impossible numbers from each cell. For each empty cell, consider which numbers 1-9 could go there, then remove any numbers already present in the same row, column, or box. The remaining candidates help you identify placements.

Step 5: Use Basic Techniques

Apply techniques like single candidates (cells with only one possible number) and single positions (numbers that can only go in one cell within a unit). These fundamental methods work by applying the three rules systematically.

Step 6: Verify Each Placement

Before placing any number, double-check that it doesn't create duplicates in its row, column, or box. This habit prevents errors that can derail your entire solution. Most digital Sudoku platforms highlight errors automatically.

Step 7: Continue Systematically

Work through the puzzle methodically, applying the three rules and basic techniques. As you fill more cells, new patterns emerge that reveal additional placements. Continue until the puzzle is complete and all 81 cells are filled correctly.

Step 8: Master Progressive Techniques

As you improve, learn intermediate techniques (pairs, triples) and advanced methods (X-Wing, Swordfish) that apply the three rules in more sophisticated ways. All techniques are based on these fundamental rules.

The Three Fundamental Rules Explained

Understanding each rule in detail:

Rule 1: Row Constraint

Each of the 9 rows must contain the digits 1-9 exactly once. No number can be repeated within the same row. When considering placing a number, check that it doesn't already appear in that row. This rule applies to all 9 rows independently.

Rule 2: Column Constraint

Each of the 9 columns must contain the digits 1-9 exactly once. No number can be repeated within the same column. When placing a number, verify it doesn't already appear in that column. This rule works alongside the row rule.

Rule 3: Box Constraint

Each of the 9 boxes (3×3 subgrids) must contain the digits 1-9 exactly once. No number can be repeated within the same box. When placing a number, ensure it doesn't already appear in that box. This rule completes the three-constraint system.

Critical Point: These three rules work together. Every number placement must satisfy all three constraints simultaneously. A number that's valid for a row but violates the column or box rule cannot be placed. This interaction between rules is what makes Sudoku puzzles solvable and challenging.

Basic Solving Techniques

Techniques that apply the three rules:

Single Candidate Technique

When a cell has only one possible number (after eliminating candidates from its row, column, and box), that number must go there. This technique directly applies all three rules through elimination.

Single Position Technique

When a number can only go in one cell within a row, column, or box (even if that cell has other candidates), that number must go there. This technique uses the rule that each number must appear exactly once in each unit.

Elimination Method

Systematically eliminate impossible numbers from each cell. For each empty cell, consider which numbers 1-9 could go there, then remove any numbers already present in the same row, column, or box. The remaining candidates reveal placements.

Common Rule Violations

Mistakes to avoid:

Placing duplicate numbers: Never place a number that already appears in the same row, column, or box
Forgetting to check all three constraints: Always verify row, column, and box rules before placing any number
Guessing instead of using logic: Every placement should be based on the three rules and elimination, not intuition
Ignoring box constraints: Beginners often focus on rows and columns but forget the box rule
Not verifying placements: Double-check each number placement to ensure it satisfies all three rules

Examples

Practical examples demonstrating Sudoku rules:

Example 1: Applying All Three Rules

You're considering placing the number 5 in a cell. First, check if 5 already appears in that row—if yes, the placement violates Rule 1. Next, check if 5 appears in that column—if yes, it violates Rule 2. Finally, check if 5 appears in that box—if yes, it violates Rule 3. Only if 5 is absent from all three units is the placement valid.

Example 2: Single Candidate Through Elimination

A row contains numbers 1, 2, 3, 4, 6, 7, 8, 9, with one empty cell. The missing number is 5. If that empty cell's column contains 1, 2, 3, 4, 6, 7, 8, 9 (no 5), and its box also doesn't contain 5, then 5 must go in that cell. This satisfies all three rules.

Example 3: Rule Interaction

An empty cell's row contains 2, 4, 7; its column contains 1, 5, 8; its box contains 3, 6, 9. By checking all three rules, you find that no number from 1-9 can be placed here without violating at least one rule. This indicates an error in previous placements, demonstrating how the rules work together to validate solutions.

Summary

Sudoku rules are elegantly simple: three fundamental constraints that every number placement must satisfy. Each row, column, and 3×3 box must contain the digits 1-9 exactly once, with no repetitions. These rules work together to create solvable puzzles that can be completed through pure logic without guessing.

Understanding how the three rules interact is the foundation of all Sudoku solving. By applying these rules systematically through techniques like single candidates and elimination, you can solve puzzles at any difficulty level. Start with easy puzzles to build confidence, use pencil marks to track candidates, and always verify each placement satisfies all three rules. With practice, applying these rules becomes intuitive, and you'll find yourself solving puzzles faster and more confidently.

Ready to start solving? Try our online Sudoku puzzles and begin applying these rules today!

❓ FAQ

Q1: What are the three basic rules of Sudoku?

The three rules are: (1) Each row must contain digits 1-9 exactly once, (2) Each column must contain digits 1-9 exactly once, and (3) Each 3×3 box must contain digits 1-9 exactly once. Every number placement must satisfy all three rules simultaneously.

Q2: Can I repeat numbers in the same row, column, or box?

No. The fundamental rule of Sudoku is that each number 1-9 must appear exactly once in every row, every column, and every 3×3 box. Repetition violates the rules and creates an invalid puzzle.

Q3: Do I need to use all numbers 1-9 in each row, column, and box?

Yes. Each row, column, and box must contain exactly one of each number from 1-9. You cannot skip numbers or use numbers outside the 1-9 range. This requirement is what makes puzzles solvable.

Q4: What happens if I place a number that violates a rule?

If you place a number that creates a duplicate in a row, column, or box, you've made an error. This will eventually lead to a contradiction (like having no valid number for a cell). Most digital Sudoku platforms highlight errors immediately. On paper, you'll need to backtrack and correct the mistake.

Q5: Can I solve Sudoku by guessing numbers?

No. Every valid Sudoku puzzle is solvable through pure logic using the three rules. Guessing is never necessary and often leads to errors. Always use logical deduction based on the rules and elimination techniques.

Q6: How do the three rules work together?

The three rules create a system of constraints. Every cell must satisfy row, column, and box rules simultaneously. A number valid for a row but invalid for its column or box cannot be placed. This interaction between rules is what makes puzzles solvable and challenging.

Q7: Are Sudoku rules the same for all difficulty levels?

Yes. All Sudoku puzzles, regardless of difficulty, follow the same three rules. Easy puzzles have more given numbers, making rule application simpler. Hard puzzles have fewer clues, requiring more advanced techniques, but the fundamental rules remain unchanged.

Q8: How do I know if I'm applying the rules correctly?

If you're applying rules correctly, each placement will be logically deducible, you won't create duplicates, and you'll eventually solve the puzzle without contradictions. If you find yourself stuck or creating duplicates, review your placements and ensure each satisfies all three rules.

Ready to get started? Try our online Sudoku game, explore daily challenges, or check out our leaderboard to see how you rank!