Introduction
Candidate mode, also called pencil marks or candidate notation, is essential for solving medium to hard Sudoku puzzles. This technique involves writing small numbers in cells to track which numbers could possibly go there. Mastering candidate mode significantly improves your ability to solve challenging puzzles in Sudoku by enabling pattern recognition and advanced technique application.
Candidate notation transforms puzzle solving from guesswork to systematic logical analysis. By tracking all possibilities, you can identify patterns, apply elimination logic, and recognize advanced techniques that aren't visible without notation. Learning to use candidate mode effectively is a crucial skill for progressing beyond beginner puzzles.
What Is Candidate Mode
Candidate mode is the practice of writing small numbers (candidates) in cells to track which numbers could possibly occupy each cell based on row, column, and box constraints. These pencil marks show all possibilities before elimination, enabling pattern recognition and systematic solving. Candidate notation is called "pencil marks" because they're traditionally written lightly with pencil for easy erasure.
Effective candidate notation includes all possible numbers for each empty cell, updated as eliminations occur. This notation enables identifying patterns like naked pairs (two cells with same two candidates), hidden pairs (two numbers restricted to two cells), and advanced techniques like X-Wing and Y-Wing. Without candidate notation, these patterns are nearly impossible to recognize.
Key Points
Point 1: Systematic Notation Ensures Completeness
Write candidates systematically, checking each cell's row, column, and box constraints. Ensure all possible numbers are noted initially, then update notation as eliminations occur. Complete notation prevents missing patterns and enables accurate technique application.
Point 2: Efficient Notation Balances Speed and Completeness
Balance notation completeness with solving speed. Some solvers use full notation (all candidates), while others use minimal notation (key candidates only). Find your optimal approach through practice. Efficient notation maintains solving speed while enabling pattern recognition.
Point 3: Candidate Tracking Enables Pattern Recognition
Proper notation makes patterns visible: naked pairs, hidden pairs, X-Wing, Y-Wing, and more. These patterns aren't obvious without candidate tracking. Learning to recognize patterns through notation is essential for advanced solving.
Point 4: Regular Updates Maintain Accuracy
Update candidate notation as you place numbers and make eliminations. Each number placement eliminates that candidate from related cells. Keeping notation current ensures accuracy and prevents errors. Regular updates maintain notation usefulness throughout solving.
Point 5: Practice Develops Notation Efficiency
Regular practice with candidate mode improves notation speed and accuracy. As you become experienced, notation becomes faster and more intuitive. Practice develops efficient notation methods that balance completeness with solving speed.
How It Works (Step-by-Step)
Step 1: Scan and Add Initial Candidates
Scan each empty cell, checking which numbers 1-9 could possibly go there based on row, column, and box constraints. Write small candidate numbers in each cell showing all possibilities. This initial notation provides the foundation for pattern recognition and elimination.
Step 2: Update Notation After Placements
When you place a number, eliminate that candidate from all cells in the same row, column, and box. Update candidate notation immediately to maintain accuracy. Regular updates ensure notation reflects current puzzle state and enables continued pattern recognition.
Step 3: Use Notation to Identify Patterns
Scan candidate notation to identify patterns: naked pairs (two cells with same two candidates), hidden pairs (two numbers in two cells), and advanced patterns like X-Wing and Y-Wing. Notation makes these patterns visible, enabling technique application.
Step 4: Apply Eliminations Based on Patterns
When you identify patterns, apply eliminations and update notation accordingly. Naked pairs eliminate those candidates from other cells in the region. Hidden pairs eliminate other candidates from the pair cells. Advanced patterns create more complex eliminations.
Step 5: Continue Solving with Updated Notation
After eliminations, continue solving using updated notation. New patterns may emerge, or single candidates may appear. Maintain notation accuracy throughout solving to enable continued progress and pattern recognition.
Examples
Example 1: Initial Candidate Notation
In a medium puzzle, cell R5C5 is empty. Checking row 5, numbers 1, 2, 3, 4, 6, and 9 are present, so 5, 7, and 8 are possible. Checking column 5, numbers 1, 2, 3, 4, 5, and 9 are present, so 6, 7, and 8 are possible. Checking box 5, numbers 1, 2, 3, 4, 5, and 9 are present, so 6, 7, and 8 are possible. Therefore, R5C5 could be 6, 7, or 8. Write these candidates as small numbers in the cell.
Example 2: Identifying Naked Pair Through Notation
In box 4, candidate notation shows cells R4C1 and R4C2 both contain only candidates 3 and 7. This is a naked pair visible through notation. Eliminate 3 and 7 from all other cells in box 4. This elimination may reveal single candidates or create other patterns.
Example 3: Hidden Pair Recognition
In row 6, candidate notation shows numbers 4 and 9 can only appear in cells R6C3 and R6C7. All other cells in row 6 cannot contain 4 or 9 due to column and box constraints. This is a hidden pair. Eliminate all other candidates from R6C3 and R6C7, leaving only 4 and 9 in both cells.
Summary
Candidate mode is essential for solving medium to hard Sudoku puzzles, enabling pattern recognition and advanced technique application. Systematic notation, regular updates, and pattern recognition through candidates significantly improve solving ability. Mastering candidate mode transforms puzzle solving from guesswork to systematic logical analysis.
Regular practice with candidate notation develops efficiency and accuracy, making pattern recognition faster and more intuitive. Learning to use candidate mode effectively is crucial for progressing beyond beginner puzzles and tackling challenging Sudoku grids.
Practice candidate mode in Sudoku, then explore more techniques in Sudoku Tips and Strategies: Complete Guide and 11 Advanced Sudoku Strategies and Examples. For different puzzles, try Number Puzzle or Word Puzzle.
FAQ (Frequently Asked Questions)
Q1: When should I start using candidate mode?
Start using candidate mode when basic techniques (single candidates and elimination) no longer provide sufficient progress. Medium difficulty puzzles typically require candidate notation. Easy puzzles can often be solved without notation, but learning notation early helps develop the skill for harder puzzles.
Q2: Should I use full notation or minimal notation?
Both approaches work. Full notation (all candidates) provides complete information but takes more time. Minimal notation (key candidates) is faster but may miss some patterns. Experiment to find your optimal approach. Many solvers use full notation for hard puzzles and minimal notation for easier ones.
Q3: How do I keep notation organized?
Write candidates in consistent positions (typically small numbers in corners or centers of cells). Use clear, legible writing. Some solvers use systematic arrangements (1-3 top, 4-6 middle, 7-9 bottom). Find an organization method that works for you and maintain consistency.
Q4: How often should I update candidate notation?
Update notation immediately after placing numbers and making eliminations. Regular updates maintain accuracy and enable continued pattern recognition. Don't let notation become outdated, as this leads to errors and missed opportunities. Consistent updates are essential for effective candidate mode use.
Q5: Can I solve puzzles without candidate notation?
Easy puzzles can often be solved without notation, but medium to hard puzzles typically require candidate tracking. Advanced techniques like X-Wing and Y-Wing are nearly impossible without notation. Learning candidate mode is essential for progressing beyond beginner puzzles.
Q6: How do I improve my candidate notation speed?
Practice regularly to improve notation speed. Start with easier puzzles to develop the skill, then progress to harder puzzles. As you become experienced, notation becomes faster and more intuitive. Focus on accuracy first, then speed develops naturally with practice.
Next Steps
Ready to master candidate mode? Play Sudoku now and practice using candidate notation on medium difficulty puzzles. For more techniques, read Sudoku Tips and Strategies: Complete Guide and 11 Advanced Sudoku Strategies and Examples. Explore other puzzles in Number Puzzle and Word Puzzle.