Introduction
Hidden singles is an essential Sudoku technique that identifies when a number can only appear in one specific cell within a row, column, or box, even though that cell contains other candidates. This technique is called "hidden" because the single isn't obvious—the cell appears to have multiple possibilities, but one number is actually restricted to just that cell. Learning hidden singles significantly improves your ability to solve puzzles in Sudoku, making it a fundamental skill for all solvers.
Hidden singles work alongside naked singles (cells with only one candidate) to provide comprehensive solving coverage. While naked singles are obvious, hidden singles require careful analysis to identify. Mastering both techniques enables efficient puzzle solving.
What Is Hidden Singles Technique
Hidden singles is a Sudoku solving technique that identifies when a number can only appear in one specific cell within a row, column, or box, even though that cell contains other candidates. The technique is called "hidden" because the single isn't immediately obvious—the cell appears to have multiple possibilities, but careful analysis reveals one number is restricted to just that cell.
When you identify a hidden single, you can place that number in the cell, eliminating other candidates. This placement is based on logical necessity: if a number can only go in one cell, that cell must contain that number, making other candidates impossible. Hidden singles often appear after other eliminations narrow possibilities.
Key Points
Point 1: Hidden Singles Require Number Restriction
For a hidden single to exist, a specific number must be able to appear in only one cell within a region. This restriction occurs when other cells in that region cannot contain the number due to row, column, or box constraints. The restriction creates the hidden single opportunity.
Point 2: Cells Contain Other Candidates Initially
Unlike naked singles where cells obviously contain only one candidate, hidden single cells contain additional candidates. The "hidden" nature comes from these extra candidates obscuring the single. Eliminating other candidates or recognizing the restriction reveals the hidden single.
Point 3: Hidden Singles Work in All Regions
The technique applies to rows, columns, and boxes equally. Scan each region systematically to find numbers restricted to one cell. The same logical principle works regardless of region type, making hidden singles a versatile solving tool.
Point 4: Systematic Scanning Identifies Hidden Singles
Systematic scanning of each region for each number 1-9 identifies hidden singles efficiently. Check which cells in each region could contain each number. If only one cell can contain a number, you've found a hidden single.
Point 5: Hidden Singles Often Reveal After Eliminations
Hidden singles frequently appear after other eliminations narrow possibilities. As you eliminate candidates, number restrictions become clearer, revealing hidden singles. This cascading effect creates solving progress.
How It Works (Step-by-Step)
Step 1: Scan a Region for Number Restrictions
Choose a row, column, or box to examine. For each number 1-9, identify which cells in that region could contain it. Look for numbers that can only appear in one cell. This requires checking row, column, and box constraints for each number.
Step 2: Identify the Hidden Single
When you find a number that can only appear in one cell within a region, you've identified a hidden single. Verify that the number truly cannot appear elsewhere in that region. This verification ensures accurate placement.
Step 3: Place the Number
Once confirmed, place the number in that cell. This placement eliminates other candidates from that cell and creates new constraints for related cells. Hidden single placement often reveals more solving opportunities.
Step 4: Update Candidate Notation
After placing a hidden single, update candidate notation in related cells. The placement eliminates that number from cells in the same row, column, and box. Regular updates maintain notation accuracy.
Step 5: Continue Solving
After placing hidden singles, continue solving using other techniques. Hidden single placements often create naked singles, reveal other hidden singles, or create conditions for advanced techniques. Continue the solving process systematically.
Examples
Example 1: Hidden Single in a Row
In row 5, number 7 can only appear in cell R5C8. All other cells in row 5 already contain other numbers or cannot contain 7 due to column and box constraints. This is a hidden single. Even though R5C8 contains other candidates like 2, 4, and 9, it must be 7.
Example 2: Hidden Single in a Box
In box 4, number 3 can only appear in cell R6C1. Checking all cells in box 4, no other cells can contain 3 due to row and column constraints. This forms a hidden single. Placing 3 in R6C1 reveals more solving opportunities.
Example 3: Hidden Single After Elimination
After applying other eliminations, number 5 in column 7 can now only appear in cell R3C7. Previous eliminations removed 5 from other cells in column 7. This hidden single appears after other techniques narrow possibilities, demonstrating cascading solving progress.
Summary
Hidden singles is an essential Sudoku technique that identifies number restrictions not immediately obvious. By recognizing when a number can only appear in one cell, you can place numbers and simplify puzzles significantly. This technique is crucial for solving easy to medium puzzles where basic methods are primary tools.
Systematic scanning for hidden singles improves solving efficiency and enables puzzle completion. Learning to identify hidden singles quickly is fundamental to Sudoku solving. This technique works alongside naked singles to provide comprehensive solving coverage.
Practice hidden singles in Sudoku, then explore more in Sudoku Tips and Strategies: Complete Guide and Intermediate Sudoku Techniques: Boost Solving Skills. For different puzzles, try Number Puzzle or Word Puzzle.
FAQ (Frequently Asked Questions)
Q1: How do I distinguish hidden singles from naked singles?
Naked singles are obvious—a cell contains only one candidate with no other possibilities. Hidden singles are "hidden" because the cell contains additional candidates, but one number is restricted to just that cell. Hidden singles require recognizing number restrictions, not just seeing single candidates.
Q2: Do I need candidate notation to find hidden singles?
Candidate notation helps but isn't always necessary for hidden singles. You can identify hidden singles by scanning regions and checking which cells could contain each number. However, notation makes hidden single identification much easier and more efficient.
Q3: How often do hidden singles appear in puzzles?
Hidden singles appear regularly in easy to medium difficulty puzzles. In easy puzzles, you might find many hidden singles. In medium puzzles, hidden singles appear frequently and are essential for efficient solving. They're fundamental techniques for all difficulty levels.
Q4: Should I look for hidden singles before or after other techniques?
Look for hidden singles alongside other basic techniques. Scan for both naked singles and hidden singles systematically. Both techniques work together to provide comprehensive solving coverage. Regular scanning for hidden singles ensures no opportunities are missed.
Q5: Can hidden singles work with more than one number?
Hidden singles specifically refer to one number restricted to one cell. However, you might find multiple hidden singles in different regions of the same puzzle. Each hidden single is independent, but finding one often reveals others.
Q6: What if I can't find any hidden singles?
If you can't find hidden singles, ensure you're scanning systematically. Check each region for each number 1-9. Sometimes hidden singles don't exist in a particular puzzle state, so continue with other techniques. They often appear after other eliminations.
Next Steps
Ready to master hidden singles? Play Sudoku now and practice identifying hidden single patterns in puzzles. For more techniques, read Sudoku Tips and Strategies: Complete Guide and Intermediate Sudoku Techniques: Boost Solving Skills. Explore other puzzles in Number Puzzle and Word Puzzle.