Intermediate Technique

Hidden Pairs

Discover pairs of numbers that can only appear in two specific cells, even when other candidates are present.

What are Hidden Pairs?

Hidden Pairs occur when two numbers can only be placed in two specific cells within a row, column, or 3x3 box, but these cells may contain other candidate numbers as well. Unlike Obvious Pairs, the pair is "hidden" among other candidates.

When you find a Hidden Pair, you can eliminate all other candidates from those two cells, leaving only the pair numbers.

How to Identify Hidden Pairs

1

Examine candidate possibilities

Look at all empty cells in a row, column, or box and identify where each number can go.

2

Find restricted pairs

Look for two numbers that can only appear in exactly two cells within the same group.

3

Eliminate other candidates

Remove all other candidate numbers from those two cells, leaving only the hidden pair.

Example: Hidden Pair in Action

Let's examine this row where we have a Hidden Pair:

Before: Finding the Hidden Pair

5
12 6 79
3
12 4 8
46 89
12 5 7
456 79
456 89
456 78

Analysis: Numbers 1 and 2 (highlighted in yellow) can only appear in cells 4 and 6 of this row, even though these cells have other candidates.

After: Eliminating Other Candidates

5
6 79
3
12
46 89
12
456 79
456 89
456 78

Result: Cells 4 and 6 now only contain candidates 1 and 2, forming a cleaner pair that can help solve other cells.

Step-by-Step Application

  1. Choose a group: Select a row, column, or 3x3 box with several empty cells
  2. Track number positions: For each missing number, identify which cells it could go in
  3. Look for pairs: Find two numbers that can each only go in the same two cells
  4. Verify the hidden pair: Ensure no other cells in the group can contain these numbers
  5. Clean up candidates: Remove all other candidates from the two cells containing the hidden pair
  6. Continue solving: The cleaned cells may now reveal obvious singles or other techniques

⚠️ Common Mistakes

  • Incomplete checking: Make sure the two numbers truly can't go anywhere else in the group
  • Missing hidden pairs: Don't forget to check all three groups (row, column, box) for each empty cell
  • Over-elimination: Only remove candidates from the two cells that form the hidden pair
  • Confusing with obvious pairs: Hidden pairs may have additional candidates that need to be eliminated

🎯 Practice Exercise

Look for Hidden Pairs in your next Sudoku puzzle:

  1. Choose a row, column, or box with 4-6 empty cells
  2. Write down candidates for each empty cell
  3. For each missing number, mark which cells it could go in
  4. Look for pairs of numbers restricted to the same two cells
  5. Eliminate other candidates from those cells

Tip: Hidden Pairs are often found in groups where many numbers have already been placed, leaving fewer possibilities for the remaining numbers.

When to Use Hidden Pairs

  • After basic techniques have been exhausted
  • When you have rows, columns, or boxes with multiple empty cells
  • When candidate lists are getting complex and need simplification
  • As preparation for more advanced techniques like X-Wing or Y-Wing

Related Techniques

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