Introduction
The rule of 3 is a key Sudoku strategy that identifies three-cell patterns creating logical eliminations. This strategy encompasses naked triples, hidden triples, and pointing triples—all using three-cell relationships to eliminate candidates. Understanding the rule of 3 significantly improves your ability to solve medium to hard puzzles in Sudoku, making it an essential technique for progressing beyond basic methods.
The rule of 3 builds upon pair techniques, extending logic to three cells. This extension provides more powerful eliminations and enables solving puzzles where pair techniques are insufficient. Learning the rule of 3 opens up new solving possibilities.
What Is the Rule of 3
The rule of 3 in Sudoku refers to strategies that use three-cell patterns to create logical eliminations. These patterns include naked triples (three cells with same three candidates), hidden triples (three numbers restricted to three cells), and pointing triples (three-cell patterns using box constraints). All these techniques use three-cell relationships to eliminate candidates.
The rule of 3 extends pair logic to three dimensions, providing more powerful eliminations. Three-cell patterns create logical necessities that enable eliminations not possible with two-cell patterns. This extension is essential for solving medium to hard puzzles.
Key Points
Point 1: Naked Triples Eliminate Candidates
Naked triples occur when three cells in the same region contain exactly the same three candidates. These three numbers must occupy those three cells, eliminating them from all other cells in that region. Naked triples are easy to spot with proper candidate notation.
Point 2: Hidden Triples Identify Restrictions
Hidden triples occur when three numbers can only appear in three specific cells within a region, even though those cells contain other candidates. Identifying hidden triples allows eliminating other candidates from those cells, simplifying the puzzle.
Point 3: Pointing Triples Use Box Constraints
Pointing triples occur when a number in a box is restricted to three cells in one row or column. This restriction eliminates that number from other cells in that row or column outside the box. Pointing triples use box constraints to create eliminations.
Point 4: Three-Cell Patterns Create Powerful Eliminations
Three-cell patterns create more powerful eliminations than two-cell patterns. The rule of 3 extends pair logic, providing additional solving opportunities. These patterns are essential for medium to hard puzzle solving.
Point 5: Systematic Application Improves Efficiency
Systematically applying the rule of 3 improves solving efficiency. Scan for naked triples, hidden triples, and pointing triples methodically. Systematic application ensures no opportunities are missed and maximizes solving progress.
How It Works (Step-by-Step)
Step 1: Scan for Naked Triples
Look for three cells in the same region (row, column, or box) that contain exactly the same three candidates. When found, eliminate those three candidates from all other cells in that region. Naked triples are easy to spot with proper candidate notation.
Step 2: Identify Hidden Triples
For each region, check if three numbers can only appear in three specific cells. Even if those cells contain other candidates, if three numbers are restricted to just those cells, you've found a hidden triple. Eliminate all other candidates from those three cells.
Step 3: Look for Pointing Triples
In each box, check if a number is restricted to three cells in one row or column. If so, that number cannot appear elsewhere in that row or column outside the box. This pointing triple creates eliminations in rows and columns based on box constraints.
Step 4: Apply Eliminations Systematically
When you identify three-cell patterns, apply eliminations immediately and update candidate notation. Rule of 3 eliminations often reveal single candidates or create conditions for other techniques. Systematic application maximizes solving progress.
Step 5: Continue Solving with Updated Information
After applying rule of 3 eliminations, continue solving using other techniques. Three-cell pattern eliminations often create cascading solving opportunities. Continue the solving process with your updated information.
Examples
Example 1: Naked Triple Elimination
In box 5, cells R4C5, R5C5, and R6C5 all contain only candidates 2, 5, and 8. This is a naked triple, meaning 2, 5, and 8 must occupy these three cells. Therefore, eliminate 2, 5, and 8 from all other cells in box 5. This elimination reveals that R5C6 must be 3, creating further progress.
Example 2: Hidden Triple Identification
In row 6, numbers 3, 6, and 9 can only appear in cells R6C2, R6C5, and R6C8. All other cells in row 6 cannot contain 3, 6, or 9 due to column and box constraints. This is a hidden triple. Eliminate all other candidates from R6C2, R6C5, and R6C8, leaving only 3, 6, and 9 in these cells.
Example 3: Pointing Triple Elimination
In box 4, the number 7 can only appear in row 4 (cells R4C1, R4C2, and R4C3). This restriction means 7 cannot appear elsewhere in row 4 outside box 4. Eliminate 7 from R4C7, R4C8, and R4C9. This elimination may reveal new solving opportunities.
Summary
The rule of 3 is a key Sudoku strategy that uses three-cell patterns to create logical eliminations. Naked triples, hidden triples, and pointing triples all use three-cell relationships to eliminate candidates and simplify puzzles. This strategy is essential for solving medium to hard puzzles where pair techniques are insufficient.
Systematic application of the rule of 3 improves solving efficiency and enables puzzle completion. Learning to recognize and apply three-cell patterns significantly improves solving ability. These patterns provide essential tools for progressing beyond basic methods.
Practice the rule of 3 in Sudoku, then explore more in Sudoku Hidden Triples Technique: Examples and Guide and Intermediate Sudoku Techniques: Boost Solving Skills. For different puzzles, try Number Puzzle or Word Puzzle.
FAQ (Frequently Asked Questions)
Q1: What is the rule of 3 in Sudoku?
The rule of 3 refers to strategies using three-cell patterns to create logical eliminations. These patterns include naked triples (three cells with same three candidates), hidden triples (three numbers restricted to three cells), and pointing triples (three-cell patterns using box constraints).
Q2: How is rule of 3 different from pair techniques?
Rule of 3 extends pair logic to three cells, providing more powerful eliminations. Naked triples work like naked pairs but with three cells. Hidden triples work like hidden pairs but with three numbers. The extension to three dimensions creates additional solving opportunities.
Q3: Do I need candidate notation for rule of 3?
Yes, candidate notation is essential for rule of 3. Without seeing all possible candidates in cells, identifying naked triples, hidden triples, and pointing triples is nearly impossible. Proper notation makes rule of 3 application much more efficient and accurate.
Q4: How often do rule of 3 patterns appear?
Rule of 3 patterns appear regularly in medium to hard difficulty puzzles. Naked triples and hidden triples are common, while pointing triples appear less frequently but provide valuable eliminations. These patterns are essential for efficient medium puzzle solving.
Q5: Should I learn rule of 3 before or after pair techniques?
Learn pair techniques first, then progress to rule of 3. Pair techniques are simpler and provide foundation for understanding three-cell patterns. Once comfortable with pairs, rule of 3 becomes more accessible. Progressive learning builds skills systematically.
Q6: Can rule of 3 work with more than three cells?
The rule specifically refers to three-cell patterns. However, the same principle extends to quads (four cells) and higher, though these are less common. Rule of 3 provides the most common and useful extension beyond pairs.
Next Steps
Ready to master the rule of 3? Play Sudoku now and practice three-cell pattern recognition on medium difficulty puzzles. For more techniques, read Sudoku Hidden Triples Technique: Examples and Guide and Intermediate Sudoku Techniques: Boost Solving Skills. Explore other puzzles in Number Puzzle and Word Puzzle.