Solving Tips

Hidden Single: Find the Only Position for a Number

2025-01-22 · 5 min read
Knowledge Base / Techniques Index / Hidden Single

Hidden Single is one of the most fundamental and practical techniques in Sudoku. The core idea is: start from a specific number and check where it can be placed in a row, column, or box. When you find that the number can only go in one position, that position's answer is determined.

Core Principle:
Sudoku rules require that each row, column, and box must contain all digits from 1-9. Therefore, when we find through elimination that a number has only one possible position in a unit, that position must contain that number.
Hidden Single Animation
Hidden Single illustration: Start from a number, scan the region to find its only possible position

Before reading this article, we recommend learning about Sudoku naming conventions for rows, columns, and boxes, which will help you understand the analysis examples below.

Hidden Single vs Naked Single

Before learning Hidden Single, let's distinguish the thinking approaches of these two basic techniques:

Comparison Hidden Single Naked Single
Starting Point Start from the number Start from the cell
Core Question "Where can this number go?" "What can go in this cell?"
Condition A number has only one possible position in a region A cell has only one candidate left
Cell's Candidates Target cell may have multiple candidates Target cell has only one candidate
Memory Tip:
  • Hidden Single: Focus on the number → "The digit 1 can only go here in this row"
  • Naked Single: Focus on the cell → "This cell can only be 1"

Example 1: Row Hidden Single

Let's look at the first example, determining the position of digit 1 by analyzing Row 3.

Sudoku Hidden Single Example - Row Analysis
Figure 1: In Row 3, the digit 1 can only go in R3C6
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Analysis Process

We need to find where digit 1 should go in Row 3. Row 3 spans from R3C1 to R3C9. Let's check each position:

1 Exclude filled cells: R3C2=8, R3C5=2, R3C9=4 are given numbers, cannot contain 1.
2 Check candidates in empty cells: See if remaining empty cells contain digit 1:
  • R3C1: Candidates {3,7}, does not contain 1 ✗
  • R3C3: Candidates {5,6,7}, does not contain 1 ✗
  • R3C4: Candidates {3,5,6,9}, does not contain 1 ✗
  • R3C6: Candidates {1,5,6,9}, contains 1 ✓
  • R3C7: Candidates {3,9}, does not contain 1 ✗
  • R3C8: Candidates {3,5,9}, does not contain 1 ✗
3 Determine unique position: Among all empty cells in Row 3, only R3C6 has digit 1 in its candidates.
Conclusion:
Hidden Single: In Row 3, digit 1 can only go in R3C6.
Therefore R3C6 = 1.

Example 2: Box Hidden Single

Now let's look at another example, determining the position of digit 2 by analyzing Box 8.

Sudoku Hidden Single Example - Box Analysis
Figure 2: In Box 8, the digit 2 can only go in R8C4
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Analysis Process

We need to find where digit 2 should go in Box 8. Box 8 contains cells R7C4-R7C6, R8C4-R8C6, R9C4-R9C6. Let's check each one:

1 Exclude filled cells: Filled cells in Box 8: R7C4=8, R7C5=4, R7C6=5, R8C6=3.
2 Check candidates in empty cells: See if remaining empty cells contain digit 2:
  • R8C4: Candidates {2,7,9}, contains 2 ✓
  • R8C5: Candidates {1,9}, does not contain 2 ✗
  • R9C4: Candidates {6,7,9}, does not contain 2 ✗
  • R9C5: Candidates {1,6,9}, does not contain 2 ✗
  • R9C6: Candidates {6,9}, does not contain 2 ✗
3 Determine unique position: Among all empty cells in Box 8, only R8C4 has digit 2 in its candidates.
Conclusion:
Hidden Single: In Box 8, digit 2 can only go in R8C4.
Therefore R8C4 = 2.

How to Find Hidden Singles?

Finding Hidden Singles requires a systematic approach:

1 Choose a number: Select a number from 1-9 to analyze. It's recommended to start with numbers that appear more frequently.
2 Choose a region: Select a row, column, or box to analyze.
3 Scan possible positions: In that region, check if each empty cell's candidates include the target number.
4 Check uniqueness: If only one empty cell's candidates contain that number, it's a Hidden Single.
Important Notes:
  • Hidden Single can be applied to rows, columns, and boxes
  • The found cell may have multiple candidates, but the target number has only this one position in the region
  • Start analyzing from regions with more filled numbers for higher success rate

Technique Summary

Key points for applying Hidden Single:

  • Thinking direction: Start from the number, ask "Where can this number go in this region?"
  • Condition: A number has only one possible position in a row/column/box
  • Three types: Row Hidden Single, Column Hidden Single, Box Hidden Single
  • Application: The most fundamental Sudoku technique, applicable to all difficulty levels
Practice Now:
Start a Sudoku game and try using Hidden Single to find answers! We recommend starting with easy difficulty to master this basic technique first.
Naked Single Techniques Index Start Game