Solving Tips

Hidden Pairs Technique: Uncovering Hidden Candidate Combinations

2025-01-24 · 7 min read

Hidden Pairs is a very practical intermediate Sudoku technique. Unlike Naked Pairs, Hidden Pairs focuses on the distribution of numbers rather than the candidates in cells. The core idea is: when two candidates only appear in the same two cells within a unit (row, column, or box), those two cells must contain these two numbers, so other candidates can be eliminated from these two cells.

         Core Principle:

        If two candidates (such as 3 and 8) only appear in two specific cells within a row, column, or box, then these two numbers must occupy those two cells. Even if the cells have other candidates, those other candidates must be eliminated because the cells can only contain these two "hidden" numbers.

Hidden Pairs Diagram: Two numbers only appear in the same two cells, eliminate other candidates from these cells

Before reading this article, we recommend understanding Sudoku naming conventions, which will help you understand the analysis examples below.

Example 1: Hidden Pair in a Column

Let's look at the first example, finding a Hidden Pair in Column 7.

Figure 1: Candidates 3 and 8 only appear in R5C7 and R8C7 in Column 7

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Analysis Process

1 Observe number distribution: Examining Column 7, we find that candidates 3 and 8 only appear in cells R5C7 and R8C7.

2 Understand the principle: Since 3 and 8 must be placed somewhere in Column 7, and only R5C7 and R8C7 contain these candidates, R5C7 and R8C7 must contain 3 and 8 (one contains 3, the other contains 8).

3 Check current candidates: From the diagram we can see:

R5C7 has candidates {3, 8, 9}
R8C7 has candidates {3, 8, 9}

4 Perform elimination: Since R5C7 and R8C7 can only contain 3 or 8, all other candidates can be eliminated from these cells:

Eliminate candidate 9 from R5C7
Eliminate candidate 9 from R8C7

Conclusion:
In Column 7, candidates 3 and 8 only appear in R5C7 and R8C7, forming a Hidden Pair.
Action: Eliminate candidate 9 from R5C7; eliminate candidate 9 from R8C7.
After elimination, these two cells' candidates simplify to {3, 8}.

Example 2: Hidden Pair in a Box

Now let's look at another example, finding a Hidden Pair in Box 4 (the middle-left 3×3 region).

Figure 2: Candidates 3 and 5 only appear in R4C1 and R5C3 in Box 4

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Analysis Process

1 Observe number distribution: Examining Box 4 (R4C1-R6C3 region), we find that candidates 3 and 5 only appear in cells R4C1 and R5C3.

2 Understand the principle: Since 3 and 5 must be placed somewhere in Box 4, and only R4C1 and R5C3 contain these candidates, R4C1 and R5C3 must contain 3 and 5.

3 Check current candidates: From the diagram we can see:

R4C1 has candidates {2, 3, 5, 8, 9}
R5C3 has candidates {1, 2, 3, 5}

4 Perform elimination: Since R4C1 and R5C3 can only contain 3 or 5, all other candidates can be eliminated from these cells:

Eliminate candidates 2, 8, 9 from R4C1
Eliminate candidates 1, 2 from R5C3

Conclusion:
In Box 4, candidates 3 and 5 only appear in R4C1 and R5C3, forming a Hidden Pair.
Action: Eliminate candidates 2, 8, 9 from R4C1; eliminate candidates 1, 2 from R5C3.
After elimination, these two cells' candidates simplify to {3, 5}.

Hidden Pairs vs Naked Pairs

Let's compare the differences between these two pair techniques:

Comparison	Naked Pairs	Hidden Pairs
Focus	Candidates in cells	Distribution of numbers in units
Recognition Pattern	Two cells with identical candidates, only 2 numbers	Two numbers only appear in the same two cells
Elimination Target	Eliminate these two numbers from other cells in the unit	Eliminate other candidates from these two cells
Why "Hidden"	Candidate pair is "naked" and visible	Number pair is "hidden" by other candidates
Difficulty	Easier (look at cells)	Harder (need to track number distribution)

         Why "Hidden"?

        Because the pairing relationship between these two numbers is "hidden" by other candidates. On the surface, the candidates in these two cells might be {2,3,5,8,9} and {1,2,3,5}, appearing unrelated. But careful analysis reveals that 3 and 5 only appear in these two cells, revealing their pairing relationship.

How to Find Hidden Pairs?

Finding Hidden Pairs requires a systematic approach:

1 Choose a unit: Select a row, column, or box to analyze.

2 Count candidate distribution: For each candidate (1-9) in that unit, count which cells contain it.

3 Look for pairs: Find two numbers that only appear in exactly the same two cells.

4 Confirm and eliminate: Once a Hidden Pair is found, eliminate all other candidates from these two cells.

Important Notes:

The two numbers must appear in exactly the same two cells
If 3 appears in R4C1, R5C3, R6C2, but 5 only appears in R4C1, R5C3, they do not form a Hidden Pair
These two cells may have many other candidates - don't be confused by them
Hidden Pairs are harder to find than Naked Pairs - patience is needed

Technique Summary

Key points for applying Hidden Pairs:

Perspective: Observe from the numbers' viewpoint, not the cells'
Recognition condition: Two numbers only appear in the same two cells within a unit
Elimination target: Eliminate other candidates from these two cells (not from other cells)
Analysis method: Systematically track each candidate's distribution in the unit
Practical value: Can significantly simplify complex cells' candidates and break through solving bottlenecks

Advanced: Hidden Triples

Hidden Pairs can be extended to Hidden Triples: When three candidates only appear in the same three cells within a unit, those cells must contain these three numbers, and other candidates can be eliminated. For example, if 2, 5, and 7 only appear in cells A1, A3, and A7, then the candidates in these three cells can only be combinations of 2, 5, and 7.

Practice Now:
Start a Sudoku game and try using Hidden Pairs to simplify complex candidates! Select a row, column, or box in the game, systematically analyze each number's distribution, and see if you can find hidden pairs.

Naked Pairs Box/Line Reduction Techniques Index