Single Candidate Technique: The Foundation
Introduction
Master the single candidate technique, the most fundamental and commonly used solving method in Sudoku puzzles.
What Is the Single Candidate Technique?
The single candidate technique (also known as "naked single") is the most basic solving method in Sudoku. It occurs when a cell has only one possible number that can be placed in it. This happens when all other numbers 1-9 are already present in the same row, column, or 3×3 box.
Key Concept: A single candidate occurs when a cell can only contain one number because all other numbers are already present in the same row, column, or box.
Key Points
Understanding single candidate technique is essential for Sudoku solving:
- Foundation technique: The most basic solving method that forms the basis for all other techniques
- Systematic scanning: Requires checking all three units (row, column, box) to identify the missing number
- Always applicable: Single candidates appear in every puzzle and should be checked after each placement
- Pattern recognition: Learning to quickly spot single candidates dramatically improves solving speed
- Building block: Mastering this technique makes learning advanced methods much easier
How It Works (Step-by-Step)
Here's the systematic approach to identifying and using single candidates:
Step 1: Choose an Empty Cell
Start with any empty cell in the puzzle. It's most efficient to work systematically, checking rows, columns, or boxes in order.
Step 2: Check the Row
Look at the row containing the cell and note which numbers 1-9 are already present. Eliminate these numbers from consideration.
Step 3: Check the Column
Look at the column containing the cell and note which numbers 1-9 are already present. Further eliminate these numbers.
Step 4: Check the 3×3 Box
Look at the 3×3 box containing the cell and note which numbers 1-9 are already present. This is the final elimination step.
Step 5: Identify the Single Candidate
If only one number is missing from all three units (row, column, box), that number must go in the cell. Place it immediately and continue solving.
Step 6: Repeat After Each Placement
After placing any number, scan for new single candidates that may have appeared in related cells.
Additional Tips for Finding Single Candidates
To find single candidates efficiently, remember these key points:
- Systematic scanning: Check rows, columns, and boxes methodically
- After each placement: New single candidates often appear after placing a number
- Visual pattern recognition: Learn to quickly spot cells with only one possibility
- Complete elimination: Ensure you've checked all three units (row, column, box) before placing
- Practice makes perfect: Regular practice improves your ability to spot single candidates quickly
Examples
Here are practical examples demonstrating single candidate technique:
Example 1: Finding a Single Candidate
In this example, let's look at the empty cell in row 1, column 3. The row contains: 5, 3, 7. The column contains: 6, 9, 8, 4, 7, 6, 2, 4. The box contains: 5, 3, 6, 9, 8. The missing number is 1, so 1 must go in this cell.
When to Use Single Candidates
Single candidates are most useful in these situations:
- Early in the Puzzle: When many numbers are already placed
- After Each Placement: Always check for new single candidates after placing a number
- When Stuck: When you can't find other obvious moves
- Systematic Solving: As part of a regular solving routine
Pro Tip: Always scan for single candidates after each number placement. New single candidates often appear after you fill in a number.
Systematic Search Method
To efficiently find single candidates, use this systematic approach:
- Row by Row: Check each row for empty cells and their possible numbers
- Column by Column: Check each column for empty cells and their possible numbers
- Box by Box: Check each 3×3 box for empty cells and their possible numbers
- Repeat: Continue until no more single candidates are found
Common Mistakes to Avoid
Beginners often make these errors when using single candidates:
- Incomplete Checking: Not checking all three units (row, column, box)
- Missing Numbers: Overlooking numbers that are already present
- Rushing: Not taking time to verify the logic
- Forgetting Updates: Not checking for new single candidates after placements
Advanced Applications
Single candidates can be combined with other techniques:
- With Pencil Marks: Use pencil marks to make single candidates easier to spot
- With Hidden Singles: Single candidates may reveal hidden singles
- With Naked Pairs: Eliminations may create new single candidates
- With Advanced Techniques: Single candidates are the foundation for more complex methods
Practice Strategies
To improve your single candidate skills:
- Start with Easy Puzzles: Practice on puzzles with many obvious placements
- Be Systematic: Use a consistent method for checking cells
- Practice Speed: Work on finding single candidates quickly
- Use Pencil Marks: Mark candidates to make single candidates more visible
- Regular Practice: Solve puzzles regularly to develop pattern recognition
Remember: Single candidates are the foundation of Sudoku solving. Mastering this technique will make all other solving methods much easier to learn and apply.
Single Candidates vs. Hidden Singles
It's important to understand the difference:
Single Candidate (Naked Single)
A cell that has only one possible number because all other numbers are already present in the same row, column, or box.
Hidden Single
A number that can only go in one cell within a unit (row, column, or box), even though that cell may have other candidates.
Single candidates are the most basic technique and should be mastered before moving on to hidden singles and other advanced methods.
Summary
The single candidate technique is the cornerstone of Sudoku solving. This fundamental method identifies cells with only one possible number by systematically checking all three units—row, column, and box. By mastering this essential technique, you'll build a solid foundation for learning more advanced solving methods and become a more efficient solver.
Single candidates appear in every puzzle and should be the first technique you check when solving. Always scan for new single candidates after each number placement, as they frequently appear as the puzzle progresses. This systematic approach transforms complex grids into solvable puzzles through logical elimination.
Ready to practice? Try our Sudoku puzzles and master the single candidate technique!
❓ FAQ
Q1: What's the difference between single candidate and hidden single?
A single candidate (naked single) occurs when a cell has only one possible number because all others are eliminated. A hidden single occurs when a number can only go in one cell within a unit, even though that cell may have other candidates too.
Q2: Do I need pencil marks to find single candidates?
Not always. Single candidates can be found by visual scanning, but pencil marks make them much easier to identify, especially in complex puzzles.
Q3: How often do single candidates appear in puzzles?
Single candidates appear frequently, especially in easy and medium puzzles. In harder puzzles, they become less common but still occur after other techniques create eliminations.
Q4: Should I check for single candidates after every placement?
Yes! After placing any number, new single candidates often appear in the same row, column, or box. Always scan for them to maintain solving momentum.
Q5: Can single candidates appear in any part of the puzzle?
Yes, single candidates can appear anywhere in the grid. Check all rows, columns, and boxes systematically to find them all.
Q6: Is single candidate the same as "naked single"?
Yes, single candidate and naked single are the same technique. "Naked single" is just another name for when a cell has only one candidate remaining.
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