Solving Tips

Hidden Single Technique: Finding the Only Position in Rows, Columns, and Boxes

2025-01-22 · 5 min read

The Hidden Single is one of the most fundamental and practical Sudoku solving techniques. The core idea is: if a number can only appear in one position within a row, column, or box, then that position must contain that number.

                 Core Principle:

                Sudoku rules require that each row, column, and box must contain all numbers from 1-9. Therefore, when we discover through elimination that a number has only one possible position in a unit, that position must be filled with that number.

Before reading this article, we recommend understanding the Sudoku naming conventions for rows, columns, and boxes, which will help you follow the examples below.

Example 1: Row Elimination

Let's look at the first example, analyzing Row 5 to determine where the number 5 belongs.

Figure 1: Finding C5 = 5 through Row 5 analysis

Analysis Process

We need to find where the number 5 should go in Row 5. Row 5 contains cells A5 through I5. Let's eliminate possibilities one by one:

1 Eliminate D5 and E5: Since E4 = 5, E5 in the same column and Box 4 cannot be 5; D5 in Box 4 also cannot be 5.

2 Eliminate H5 and I5: Since I6 = 5, both H5 and I5 in Box 6 cannot be 5.

3 Eliminate B5: Since B1 = 5, B5 in column B cannot be 5.

4 Eliminate filled cells: A5, F5, and G5 already contain other numbers.

Conclusion:
After elimination, only C5 can contain the number 5 in Row 5. Therefore, C5 = 5.

Example 2: Box Elimination

Now let's look at another example, analyzing Box 8 to determine where the number 4 belongs.

Figure 2: Finding E7 = 4 through Box 8 analysis

Analysis Process

We need to find where the number 4 should go in Box 8. Box 8 contains cells D7-F7, D8-F8, and D9-F9. Let's eliminate:

1 Eliminate D8: Since B8 = 4, D8 in Row 8 cannot be 4.

2 Eliminate D9, E9, F9: Since H9 = 4, D9, E9, and F9 in Row 9 cannot be 4.

3 Eliminate F7: Since F6 = 4, F7 in column F cannot be 4.

4 Eliminate filled cells: D7, E8, and F8 already contain other numbers.

Conclusion:
After elimination, only E7 can contain the number 4 in Box 8. Therefore, E7 = 4.

Example 3: Using Candidate Notation

In practice, we often mark candidates in empty cells—all possible numbers that could fill that cell. With candidate notation, applying the Hidden Single technique becomes more intuitive.

Hidden Single Example - Candidate Notation

Figure 3: With candidates marked, only E7 contains candidate 4 in Box 8

Analysis from Candidate Perspective

The figure above shows the same puzzle with all candidates marked. Box 8 is highlighted with a border, and the candidate 4 in E7 is marked with a green circle.

✓ Observe Box 8: Among the 9 cells in Box 8, only E7 has the number 4 in its candidates. Other cells either contain filled numbers or don't have 4 as a candidate.

Conclusion:
When a number appears in the candidates of only one cell within a box (or row/column), that cell's answer is that number. This is the essence of Hidden Single—finding the unique candidate position for a number. Therefore, E7 = 4.

                 Why is it called "Hidden Single"?

                This technique is called "Hidden Single" because the unique number is "hidden" within the candidate list. Unlike a "Naked Single" where a cell obviously has only one candidate, you need to check the entire row, column, or box to discover that this is the only possible position for that number.

Technique Summary

Hidden Single can be applied in three ways:

Row elimination: Find where a number can only appear in one position within a row
Column elimination: Find where a number can only appear in one position within a column
Box elimination: Find where a number can only appear in one position within a box

Important Note:
Hidden Single requires considering constraints from rows, columns, and boxes together. A cell may be eliminated because the same row already has that number, the same column already has that number, or the same box already has that number. Always check all three dimensions.

Practice Tips

Start analyzing from rows, columns, or boxes with more filled numbers—elimination is easier
Focus on one number at a time and systematically check all rows, columns, and boxes
Develop the habit of marking candidates to avoid missing opportunities
With practice, Hidden Single will become faster and more natural

Practice Now:
Start a Sudoku game and try using Hidden Single to find answers!

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