How To Find Hidden Pairs In Sudoku

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Hidden pairs are one of the most powerful intermediate Sudoku techniques that can dramatically speed up your solving process. When you master this technique, you'll be able to solve puzzles that seemed impossible before.

What Are Hidden Pairs?

A hidden pair occurs when two numbers can only appear in two specific cells within a row, column, or 3x3 box. While other numbers might also be possible in those cells, the key insight is that these two numbers have nowhere else to go.

Unlike naked pairs (where only two numbers are possible in two cells), hidden pairs are more subtle because the cells might contain other candidates as well.

How to Spot Hidden Pairs

To identify hidden pairs, follow these steps:

Step 1: Scan Each Unit

Look at each row, column, and 3x3 box individually. For each number (1-9), count how many cells could potentially contain that number.

Step 2: Find Numbers with Limited Options

Look for numbers that appear in exactly two cells within the same unit. If you find two different numbers that both appear in the same two cells, you've found a hidden pair!

Step 3: Eliminate Other Candidates

Once you've identified a hidden pair, remove all other possible numbers from those two cells. Only the two numbers in the pair can remain as candidates.

Example: Hidden Pair in a Row

Imagine a row where:

  • Cell A has candidates: 2, 4, 7
  • Cell B has candidates: 1, 3, 5
  • Cell C has candidates: 2, 4, 8
  • Cell D has candidates: 6, 9
  • Cell E has candidates: 1, 3, 5

Looking at this row, we notice that numbers 2 and 4 only appear in cells A and C. This means 2 and 4 form a hidden pair in those two cells.

We can now eliminate all other candidates from cells A and C, leaving only 2 and 4 as possibilities in each cell.

Advanced Hidden Pair Techniques

Hidden Triples

Similar to hidden pairs, hidden triples occur when three numbers can only appear in three specific cells within a unit. This technique works the same way but is even more powerful.

Hidden Quads

In rare cases, you might find hidden quads - four numbers that can only appear in four specific cells. While less common, recognizing these patterns can solve very difficult puzzles.

Common Mistakes to Avoid

  • Confusing with Naked Pairs: Remember that hidden pairs can coexist with other candidates in the same cells.
  • Incomplete Scanning: Always check all three types of units (rows, columns, and boxes) for hidden pairs.
  • Forgetting Elimination: Once you find a hidden pair, make sure to remove other candidates from those cells.

Practice Tips

To master hidden pairs:

  • Start with easier puzzles and consciously look for hidden pairs
  • Use pencil marks to track all possible candidates
  • Practice scanning systematically through each unit
  • Don't rush - hidden pairs require careful observation

When to Use Hidden Pairs

Hidden pairs are most effective when:

  • You've exhausted basic techniques (singles and naked pairs)
  • A puzzle seems stuck but not extremely difficult
  • You have good pencil marking throughout the grid
  • You're looking to improve your intermediate solving skills

Mastering hidden pairs will significantly improve your Sudoku solving speed and help you tackle more challenging puzzles with confidence.

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