Hidden Singles: Finding Numbers in Hiding

After mastering naked singles, the next essential technique is hidden singles. While naked singles focus on cells with only one candidate, hidden singles shift your perspective to focus on the numbers themselves.

What is a Hidden Single?

A hidden single occurs when a specific number can only go in one place within a row, column, or 3×3 box - even though that cell might have multiple candidate numbers.

The Key Difference

Naked Single

• Focus: Look at a cell
• Question: "What number can go here?"
• Answer: Only one number fits

Hidden Single

• Focus: Look at a number
• Question: "Where can this number go?"
• Answer: Only one position possible

Why "Hidden"?

The number is "hidden" among other candidates in the cell. Unlike a naked single where the cell obviously has one candidate, a hidden single requires you to analyze where a specific digit can be placed.

How to Find Hidden Singles

Method 1: Scanning by Number

Pick a number (say, 5) and scan each unit:

Step 1: Choose a Row, Column, or Box Look at one unit at a time.

Step 2: Check Where the Number Can Go

• Cross out cells that already have that number in their row
• Cross out cells that already have that number in their column
• Cross out cells that already have that number in their box

Step 3: Count Remaining Cells If only ONE cell remains where the number can go, you've found a hidden single!

Method 2: Candidate Analysis

Using notes mode:

Step 1: Fill in Candidates Write all possible numbers for each empty cell.

Step 2: Scan Each Unit Look at a row, column, or box.

Step 3: Find Unique Candidates If a number appears as a candidate in only ONE cell within that unit, it must go there - even if that cell has other candidates!

Visual Examples

Example 1: Hidden Single in a Row

Row 5 currently contains: 1, 2, 3, 4, 5, 6, 7, 9
Missing number: 8

Empty cells in Row 5:
- Cell A: candidates are 2, 8
- Cell B: candidates are 2, 6, 8
- Cell C: candidates are 2, 6

Which cell must be 8?

Analysis:

• Cell A: Could be 2 or 8
• Cell B: Could be 2, 6, or 8
• Cell C: Could be 2 or 6 (no 8!)

Only cells A and B can contain 8. Now check their columns and boxes to see which one is actually valid.

If Cell B's column already has an 8, then Cell A MUST be 8. This is a hidden single!

Example 2: Hidden Single in a Box

Box (top-left 3×3) contains: 1, 3, 4, 5, 6, 7, 8, 9
Missing number: 2

Empty cells and their full candidates:
- Cell X: 2, 5, 9
- Cell Y: 5, 9
- Cell Z: 5, 9

Which cell must be 2?

Analysis: The number 2 only appears in Cell X's candidates. Even though Cell X has three possible numbers, it MUST be 2 because no other cell in this box can be 2.

This is a hidden single in the box!

Example 3: Hidden Single in a Column

Column 6:
- Row 1: 7
- Row 2: Empty (candidates: 1, 4, 8)
- Row 3: 3
- Row 4: Empty (candidates: 1, 4, 8)
- Row 5: 2
- Row 6: Empty (candidates: 1, 8)
- Row 7: 9
- Row 8: 5
- Row 9: 6

Missing number: 4

Analysis:

• Row 2's cell: can be 1, 4, or 8
• Row 4's cell: can be 1, 4, or 8
• Row 6's cell: can be 1 or 8 (no 4!)

The number 4 only appears in Rows 2 and 4. You'd need to check their rows and boxes to determine which one must be 4.

Systematic Scanning Strategy

The 1-9 Sweep

A methodical approach for finding hidden singles:

Step 1: Start with Number 1

• Scan all rows for where 1 can go
• Scan all columns for where 1 can go
• Scan all boxes for where 1 can go

Step 2: Move to Number 2 Repeat the process.

Step 3: Continue Through 9 Work through each number systematically.

Step 4: Repeat After filling in some numbers, start over from 1.

Focus on Constrained Units

Priority Scanning Look at units that are mostly filled:

• Rows with 7-8 numbers filled
• Columns with 7-8 numbers filled
• Boxes with 7-8 numbers filled

These units have fewer empty cells, making hidden singles easier to spot!

Using Super Sudoku's Features

Auto-Generated Notes

Enable in Settings: "Show auto generated notes"

How It Helps:

• Automatically displays candidate numbers
• Makes hidden singles visible at a glance
• No manual note-taking needed

Finding Hidden Singles:

1. Look at a row, column, or box
2. Pick a missing number
3. Scan the auto-generated notes
4. If that number appears in only one cell's notes, it's a hidden single!

Highlight Features

Show Occurrences When you select a number in the menu, the game highlights where that number already exists. This helps you:

• See which rows/columns/boxes already have the number
• Identify where the number is still missing
• Spot potential hidden singles

Using Hints

The hint system (press H) will often reveal hidden singles. Try to find them yourself first for better learning!

Practice Exercises

Exercise 1: Row Scanning

Row needs: 3, 5, 7
Empty cells' candidates:
- Cell A: 3, 5, 7
- Cell B: 3, 7
- Cell C: 5, 7

Find the hidden single.

Exercise 2: Box Scanning

Box needs: 1, 2, 8, 9
Empty cells' candidates:
- Cell 1: 1, 2, 8
- Cell 2: 2, 8, 9
- Cell 3: 1, 8, 9
- Cell 4: 1, 2, 9

Find all hidden singles.

Exercise 3: Column Scanning

Column needs: 4, 6
Empty cells' candidates:
- Cell X: 4, 6, 8
- Cell Y: 4, 6

Can you determine both numbers?

Common Mistakes to Avoid

Mistake 1: Forgetting to Check All Three Units

Wrong Approach: "Cell has 2 and 5 as candidates. The row needs 2, so it must be 2!"

Why It's Wrong: You must also check the column and box. Even if the row needs 2, the column might already have a 2, making it impossible.

Correct Approach: Always verify row AND column AND box.

Mistake 2: Confusing Hidden and Naked Singles

Hidden Single: Cell has multiple candidates (2, 5, 8), but only one number (say, 8) can go there when you consider the entire unit.

Naked Single: Cell has only one candidate total.

Mistake 3: Not Systematically Scanning

Random Scanning: Looking randomly for hidden singles is inefficient.

Systematic Scanning: Work through numbers 1-9 in order, or scan units (rows/columns/boxes) methodically.

Mistake 4: Missing Updates After Placement

After placing a hidden single, it creates new constraints! Always:

1. Update your mental or written candidates
2. Check if this created new naked singles
3. Scan again for new hidden singles

Advanced Tips

Combining with Naked Singles

Efficient Workflow:

1. Fill all naked singles first
2. Then scan for hidden singles
3. Filling a hidden single often creates new naked singles
4. Return to step 1

This back-and-forth is the foundation of sudoku solving!

Speed Solving Technique

Visual Scanning: Experienced solvers don't write all candidates. Instead:

1. Focus on numbers 1-9 one at a time
2. Quickly scan rows, columns, boxes
3. Spot where each number must go
4. Enter it and move to the next number

Practice this with easy puzzles to build speed!

When to Use Hidden Singles

Early Game: Hidden singles are often easier to spot in partly-filled grids.

Mid Game: As the grid fills, hidden singles become rarer but more crucial.

Late Game: Near the end, you're usually dealing with naked singles.

Real-World Application

Try It Now in Super Sudoku

1. Open an Easy puzzle
2. Enable "Show auto generated notes"
3. Pick a number (try 1)
4. Scan each box - can you find where 1 must go in each box?
5. Repeat for 2-9

Progressive Practice

Week 1: Recognition

• Focus only on finding hidden singles
• Use hints to verify
• Don't worry about speed

Week 2: Speed

• Try to find hidden singles faster
• Scan systematically
• Reduce reliance on hints

Week 3: Integration

• Combine naked and hidden singles
• Solve easy puzzles using only these techniques
• Build smooth workflow

Beyond Hidden Singles

Once you're comfortable with hidden singles, you're ready for:

Intermediate Techniques

• Naked Pairs: Two cells with identical two-candidate sets
• Hidden Pairs: Two numbers confined to two cells
• Pointing Pairs: Box-line interactions

Your Next Steps

1. Master both singles: Become fluent with naked and hidden singles
2. Build speed: Practice until it's automatic
3. Learn naked pairs: The next technique in your toolbox

Hidden singles are fundamental. Even advanced players rely heavily on this technique. Master it, and you're well on your way to solving harder puzzles!

Quick Reference

Hidden Single Checklist

• Pick a number to track (1-9)
• Choose a unit (row, column, or box)
• Find all empty cells in that unit
• Eliminate cells where the number can't go
• If only ONE cell remains → Hidden single!
• Verify by checking row, column, and box constraints

When You're Stuck

1. Enable auto-generated notes
2. Systematically scan for each number 1-9
3. Check rows, then columns, then boxes
4. Look for units that are mostly filled
5. Use the hint system to learn

Happy solving, and enjoy discovering those hidden singles! 🔍