Introduction

The Hidden Singles technique is a simple yet powerful Sudoku solving method that can be quite challenging to spot. While the concept is straightforward—a candidate appears only once in a row, column, or 3×3 block—identifying hidden singles requires careful attention and systematic scanning.

Understanding Hidden Singles is essential for efficient puzzle solving. This technique often reveals placements that aren't immediately obvious, especially when cells contain multiple candidates. By learning to recognize hidden singles, you'll be able to make progress in puzzles where other basic techniques don't reveal obvious placements.

What Is the Hidden Singles Technique?

The Hidden Singles technique applies when a candidate (a possible number shown in notes or pencil marks) appears only once in an entire row, column, or 3×3 block. When a candidate is the only one of its kind in a unit, that number must go in that specific cell, even if that cell has other candidates as well.

This technique is called "hidden" because the single candidate might not be immediately obvious—the cell containing it may have multiple candidates, making it look like other numbers could go there. However, by checking the entire row, column, or block, you discover that only one cell can contain that particular number.

Hidden Singles requires proper notes placement to identify. Without visible candidates, you cannot see that a number appears only once in a unit. This technique is particularly useful in medium-difficulty puzzles where basic single candidate methods are insufficient but advanced techniques aren't needed yet.

Key Points

Understanding these fundamentals helps you master Hidden Singles:

Requires notes: Hidden Singles can only be identified when you have proper notes (pencil marks) showing all possible candidates
Only one appearance: The candidate must appear exactly once in the entire row, column, or block—no other cells in that unit can contain it
Cell may have other candidates: The cell containing the hidden single may have multiple candidates, but that number is the only one that can go there
Careful attention needed: This technique can be hard to spot, requiring systematic scanning and careful observation
Works in all units: Hidden Singles can occur in rows, columns, or 3×3 blocks
Creates immediate placement: Once identified, you can place the number and remove other candidates from that cell

How It Works (Step-by-Step)

Follow these steps to identify and apply the Hidden Singles technique:

Step 1: Enable Notes or Pencil Marks

Start by enabling notes mode on your Sudoku grid. Fill in all possible candidates for each empty cell based on what numbers are already present in that cell's row, column, and box. Hidden Singles cannot be identified without visible notes showing all candidates.

Step 2: Scan Each Row Systematically

Work through each of the nine rows one at a time. For each row, check each number from 1 to 9. Count how many cells in that row contain each number as a candidate. If a number appears as a candidate in only one cell of the row, you've found a Hidden Single.

Step 3: Scan Each Column Systematically

After checking rows, work through each of the nine columns. For each column, check each number from 1 to 9. Count how many cells in that column contain each number as a candidate. If a number appears as a candidate in only one cell of the column, you've found a Hidden Single.

Step 4: Scan Each 3×3 Block Systematically

Finally, work through each of the nine 3×3 blocks. For each block, check each number from 1 to 9. Count how many cells in that block contain each number as a candidate. If a number appears as a candidate in only one cell of the block, you've found a Hidden Single.

Step 5: Verify the Hidden Single

Confirm that the candidate appears only once in that unit. Check all cells in the row, column, or block to ensure no other cell contains that candidate. This verification is important because missing another appearance would make this technique invalid.

Step 6: Place the Number

Once you've identified a Hidden Single, place that number in the cell. Even if the cell has other candidates, this number must go there because it's the only cell in that unit that can contain it.

Step 7: Remove Other Candidates

After placing the hidden single, remove all other candidates from that cell. The cell now contains only the placed number. Also remove this number from notes in other cells in the same row, column, and box, as it can no longer appear elsewhere.

Examples

Here are practical examples demonstrating how Hidden Singles works:

Example 1: Hidden Single in a Block

You're examining a 3×3 block with notes filled in. You check for number 1 and count how many cells contain 1 as a candidate. You find that only one cell—the top right cell—contains 1 as a candidate. There are no other cells in this block with the note 1.

Since 1 can only go in this one cell, you can remove all other notes from this cell and place number 1 there. This is a Hidden Single—the number 1 is "hidden" because the cell had other candidates, but 1 is the only number that can go in that cell within this block.

Example 2: Hidden Single in a Row

You're scanning a row and checking for number 5. You count how many cells in this row contain 5 as a candidate. You find that only one cell contains 5, even though that cell also has candidates 3, 7, and 9. Since 5 appears only once in this row, it must go in that cell.

You place 5 in that cell and remove the other candidates (3, 7, 9) from it. You also remove 5 from notes in other cells in the same column and box, as 5 can no longer appear there.

Example 3: Hidden Single in a Column

You're checking a column for number 8. After counting, you discover that only one cell in this column contains 8 as a candidate. Even though that cell has multiple candidates (2, 4, 6, 8), number 8 must go there because it's the only cell in the column that can contain 8.

You place 8 in that cell, remove the other candidates, and update notes throughout the grid accordingly.

Example 4: Not a Hidden Single

You're checking a block for number 3. You find that two cells contain 3 as a candidate. This is not a Hidden Single because the candidate appears in more than one cell. You continue scanning for other numbers or check other units.

Example 5: Multiple Hidden Singles

After placing one Hidden Single and updating notes, you continue scanning. You discover another Hidden Single in a different row—number 7 appears only once. You place 7, update notes, and continue. This process of finding Hidden Singles, placing numbers, and updating notes creates a chain reaction of placements.

How Hidden Singles Relates to Other Techniques

Hidden Singles is part of a family of related techniques:

Obvious Singles (Naked Singles)

Obvious Singles occur when a cell has only one candidate remaining. Hidden Singles is different—the cell may have multiple candidates, but one of them appears only once in the unit. Both techniques result in placing a number, but they're identified differently.

Hidden Pairs

Hidden Pairs is the extension of Hidden Singles, where two candidates appear in only two cells of a unit. Understanding Hidden Singles prepares you for learning Hidden Pairs, which uses similar logic but with two numbers instead of one.

Last Remaining Cell

Hidden Singles is similar to Last Remaining Cell technique, but Hidden Singles specifically requires checking notes to see that a candidate appears only once, while Last Remaining Cell can be identified by counting filled numbers.

When to Use Hidden Singles

Hidden Singles is most effective when:

Notes are complete: You've filled in notes for all empty cells in the unit
Obvious Singles are exhausted: After checking for cells with only one candidate, look for Hidden Singles
Medium difficulty puzzles: This technique becomes essential when progressing from easy to medium puzzles
Systematic scanning: When you scan rows, columns, and blocks methodically, Hidden Singles become easier to spot

Common Mistakes to Avoid

Avoid these errors when using Hidden Singles:

Not checking all cells: Make sure you check every cell in the unit to confirm the candidate appears only once
Missing the hidden single: This technique requires careful attention—don't rush the scanning process
Forgetting to remove other candidates: After placing the hidden single, remove other candidates from that cell
Not updating notes: After placing a number, update notes throughout the grid to see new opportunities
Confusing with Obvious Singles: Hidden Singles can have multiple candidates in the cell; Obvious Singles have only one

Tips for Finding Hidden Singles

These tips help you identify Hidden Singles more efficiently:

Scan systematically: Check each number 1-9 in each unit methodically rather than randomly
Count appearances: For each number, count how many cells contain it as a candidate in the unit
Work unit by unit: Complete one row, column, or block before moving to the next
Use visual scanning: When notes are visible, look for numbers that appear infrequently
Re-scan after placements: After placing numbers, re-scan units as new Hidden Singles may appear

Why Hidden Singles Can Be Hard to Spot

Hidden Singles can be challenging to identify because:

Cells have multiple candidates: The cell containing the hidden single may have 3-4 candidates, making it look like other numbers could go there
Requires careful counting: You must check every cell in the unit to count candidate appearances accurately
Visual clutter: With many notes visible, it's easy to miss that a number appears only once
Systematic approach needed: Random scanning makes Hidden Singles easy to miss—methodical checking is essential

Summary

The Hidden Singles technique is a simple but powerful Sudoku solving method that requires careful attention to identify. By recognizing when a candidate appears only once in a row, column, or 3×3 block, you can place numbers that might not be immediately obvious, making significant progress in puzzles.

This technique requires proper notes placement and systematic scanning to identify. While it can be challenging to spot, especially when cells contain multiple candidates, mastering Hidden Singles is essential for efficient puzzle solving. The technique works in all units and often creates chain reactions of placements as you update notes after each discovery.

Remember that Hidden Singles complements Obvious Singles—after checking for cells with only one candidate, always scan for Hidden Singles where a candidate appears only once in a unit. This systematic approach ensures you don't miss placement opportunities and helps you solve puzzles more efficiently.

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❓ FAQ

Q1: What's the difference between Hidden Singles and Obvious Singles?

Obvious Singles (Naked Singles) occur when a cell has only one candidate remaining. Hidden Singles occur when a candidate appears only once in a unit, but the cell may have multiple candidates. Both result in placing a number, but they're identified differently.

Q2: Do I need notes to find Hidden Singles?

Yes. Hidden Singles can only be identified when you have proper notes showing all possible candidates. Without visible candidates, you cannot see that a number appears only once in a unit.

Q3: Can Hidden Singles appear in rows, columns, and blocks?

Yes. Hidden Singles can occur in any unit: rows, columns, or 3×3 blocks. The same principle applies: if a candidate appears only once in a unit, that number must go in that cell.

Q4: Why are Hidden Singles hard to spot?

Hidden Singles can be difficult to identify because the cell containing them may have multiple candidates, making it look like other numbers could go there. They also require careful, systematic scanning to count candidate appearances accurately.

Q5: How do I know when to look for Hidden Singles?

Look for Hidden Singles when you've filled in notes for all empty cells and have already checked for Obvious Singles. In medium-difficulty puzzles, Hidden Singles become essential for making progress.

Q6: What if a candidate appears twice in a unit?

If a candidate appears in two or more cells of a unit, it's not a Hidden Single. The technique requires that the candidate appears exactly once. If it appears multiple times, continue scanning for other numbers or check other units.

Q7: Should I scan for Hidden Singles after every placement?

Yes. After placing any number and updating notes, re-scan for new Hidden Singles. Each placement creates new information, and new Hidden Singles may appear as candidates are removed from other cells.

Q8: Can Hidden Singles help with hard puzzles?

Yes. Hidden Singles appear in puzzles of all difficulty levels, from easy to expert. While hard puzzles require additional advanced techniques, Hidden Singles remain useful throughout and should always be checked.

Hidden Singles Technique in Sudoku: Complete Guide with Notes Strategy