Sudoku Hidden Pairs Technique: Discovering Hidden Candidate Combinations
Hidden Pairs is a highly practical intermediate Sudoku technique. Unlike Naked Pairs, Hidden Pairs focuses on number distribution rather than cell candidates. The core concept is: when two candidates appear only in the same two cells within a unit (row, column, or box), those two cells must contain these two numbers, allowing you to eliminate all other candidates from those cells.
If two candidates (e.g., 5 and 8) appear only in two specific cells within a row, column, or box, these two numbers must occupy those two cells. Even if these cells contain other candidates, those other candidates must be eliminated because the cells can only contain the two "hidden" numbers.
Before reading this article, we recommend understanding the Sudoku row, column, and box naming conventions, which will help you follow the analysis examples below.
Example 1: Hidden Pair in a Column
Let's examine the first example, where we discover a Hidden Pair in column F.
Analysis Process
In column F, candidates 5 and 8 only appear in F1 and F3, therefore the candidates in these two cells are reduced to {5, 8}, eliminating all other candidates such as 1, 2, 4, 6, 9.
Example 2: Hidden Pair in a Box
Next, let's look at another example where we discover a Hidden Pair in box 5.
Analysis Process
In box 5, candidates 1 and 6 only appear in D6 and F6, therefore the candidates in these two cells are reduced to {1, 6}, eliminating all other candidates such as 3, 7, 9.
Hidden Pairs vs Naked Pairs
Let's compare these two pair techniques:
| Comparison | Naked Pairs | Hidden Pairs |
|---|---|---|
| Focus | Cell candidates | Number distribution in unit |
| Identification | Two cells with identical candidates containing only 2 numbers | Two numbers appearing only in the same two cells |
| Elimination Target | Remove these two numbers from other cells in the unit | Remove other candidates from these two cells themselves |
| Why "Hidden" | The candidate pair is "naked" and visible | The number pair is "hidden" among other candidates |
| Difficulty | Easier (look at cells) | Harder (need to track number distribution) |
Because the pairing relationship between these two numbers is "hidden" among other candidates. On the surface, these two cells might have candidates {1,5,6,8,9} and {1,4,5,6,8}, appearing unrelated. But careful analysis reveals that numbers 5 and 8 only appear in these two cells, exposing their pairing relationship.
How to Find Hidden Pairs?
Finding Hidden Pairs requires a systematic approach:
- Must be two numbers appearing in exactly the same two cells
- If number 5 appears in F1, F3, F5, while number 8 only appears in F1, F3, they do not form a Hidden Pair
- These two cells may have many other candidates - don't be confused
- Hidden Pairs are harder to spot than Naked Pairs and require patient analysis
Technique Summary
Key points for applying the Hidden Pairs technique:
- Perspective: Observe from the numbers' perspective, not the cells' perspective
- Identification criteria: Two numbers appearing only in the same two cells within a unit
- Elimination target: Remove other candidates from these two cells (not from other cells)
- Analysis method: Systematically track each candidate's distribution within the unit
- Practical value: Can significantly simplify complex cell candidates and break through solving bottlenecks
Advanced: Hidden Triples
Hidden Pairs can be extended to Hidden Triples: when three candidates appear only in the same three cells within a unit, those three cells must contain these three numbers, allowing elimination of all other candidates from those cells. For example, if numbers 2, 5, and 7 only appear in cells A1, A3, and A7, the candidates in these three cells can only be combinations of 2, 5, and 7.
Start a Sudoku game and try using the Hidden Pairs technique to simplify complex candidates! In the game, select a row, column, or box, systematically analyze each number's distribution, and see if you can find hidden pairs.