Techniques

Sudoku Hidden Pairs Technique and Examples: Complete Guide

Tuesday, March 11, 2025

Introduction

Hidden pairs occur when two cells within the same row, column, or 3×3 block share two candidate numbers that no other cells contain. The two cells with this hidden set of numbers may contain other candidate numbers, which is why they're considered hidden. You can eliminate all other candidate numbers within these cells because logically the cells have to contain one of the two options in the hidden pair.

This Sudoku strategy is great for both beginners learning how to play and advanced players leveraging equivalence-based techniques like Phistomefel ring. Finding hidden pairs helps you eliminate candidates and solve your Sudoku puzzle more quickly, often creating chain reactions that lead to additional placements and eliminations.

What Are Hidden Pairs?

Hidden pairs are a Sudoku solving technique where two cells within the same unit (row, column, or 3×3 block) share exactly two candidate numbers that don't appear as candidates in any other cells within that unit.

Key Characteristics:

  • Two cells: The pattern involves exactly two cells
  • Same unit: Both cells must be in the same row, column, or 3×3 block
  • Two shared candidates: The cells share exactly two candidate numbers
  • Unique restriction: These two numbers don't appear as candidates in any other cells in that unit
  • Other candidates possible: The two cells may contain additional candidates (making them "hidden")

Why "Hidden": Unlike naked pairs where the two cells have only those two candidates (making them obvious), hidden pairs are "hidden" because the cells contain other candidates as well. You need to look deeper to discover that only two specific numbers can appear in those two positions.

Key Points

Essential concepts for understanding Hidden Pairs:

  • Two cells, two numbers: Exactly two cells share exactly two candidate numbers
  • Same unit requirement: Both cells must be in the same row, column, or block
  • Unique restriction: The two numbers don't appear elsewhere in that unit
  • Elimination power: Remove all other candidates from those two cells
  • Chain reactions: Often leads to additional eliminations and placements
  • Beginner to advanced: Useful for all skill levels

How to Find Hidden Pairs

Criteria for Hidden Pairs

Hidden pairs must meet the following criteria:

  1. Two cells within the same row, column, or 3×3 block share exactly two candidate numbers.

  2. The two candidate numbers do not appear in any other cells within that row, column, or block.

  3. Other candidates that are not part of the hidden pair appear in at least one of the two hidden pair cells.

Step-by-Step Identification Process

Step 1: Use Candidate Mode

Note all possible candidate numbers within each cell. Complete pencil marks are essential for identifying hidden pairs, as you need to see all possibilities to recognize the pattern.

Step 2: Scan Each Unit

Systematically scan each row, column, and 3×3 block. Look for two cells that share candidate numbers.

Step 3: Check for Shared Candidates

When you find two cells with some shared candidates, check if:

  • They share exactly two candidate numbers
  • These two numbers don't appear as candidates in any other cells in that unit

Step 4: Verify the Pattern

Confirm that the two shared numbers are unique to those two cells within the unit. If either number appears as a candidate in another cell in that unit, it's not a hidden pair.

Step 5: Apply Eliminations

Once confirmed, eliminate all other candidates from those two cells (except the two numbers in the hidden pair).

Example Identification

Scenario: In a row, you find:

  • Cell A has candidates: 1, 3, 5
  • Cell B has candidates: 2, 3, 5
  • No other cells in that row have candidates 3 or 5

Analysis:

  • Cells A and B share candidates 3 and 5
  • Numbers 3 and 5 don't appear in any other cells in that row
  • This forms a hidden pair (3, 5)

Action: Eliminate candidates 1 from cell A and candidate 2 from cell B, leaving only 3 and 5 as candidates in both cells.

Hidden Pair Examples

Hidden pairs don't just help you eliminate numbers in two cells. They often create chain reactions, allowing you to find answers and eliminate numbers elsewhere in the puzzles. As you search for hidden pairs, you may even discover a single candidate that leads to the locked candidate technique.

Example 1: Hidden Pairs in a Row

Setup:

  • Row 2 contains multiple cells with various candidates
  • Cell H2 has candidates: 1, 3, 7
  • Cell I2 has candidates: 3, 6
  • No other cells in row 2 have candidates 1 or 3

Analysis:

  • Cells H2 and I2 share candidates 1 and 3
  • Numbers 1 and 3 don't appear in any other cells in row 2
  • This forms a hidden pair (1, 3)

Elimination:

  • Remove candidate 7 from H2 (leaving only 1 and 3)
  • Remove candidate 6 from I2 (leaving only 1 and 3)

Additional Observations:

  • In addition to the hidden pair, there are two sets of naked pairs in row 2: A2 and B2 (2, 7) and E2 and F2 (6, 8)
  • If you noticed the naked pairs before the hidden pair, they also would have allowed you to eliminate the 7 in H2 and 6 in I2 because the naked pairs indicate that no other cells in that row can contain 2, 7, 6, or 8

Example 2: Hidden Pairs in a Block

Setup:

  • Center block (middle 3×3 block) contains multiple cells
  • Cell D1 has candidates: 2, 3, 5, 6, 8
  • Cell E1 has candidates: 2, 5, 8
  • No other cells in the center block have candidates 5 or 8

Analysis:

  • Cells D1 and E1 share candidates 5 and 8
  • Numbers 5 and 8 don't appear in any other cells in the center block
  • This forms a hidden pair (5, 8)

Elimination:

  • Remove candidates 2, 3, and 6 from D1 (leaving only 5 and 8)
  • Remove candidate 2 from E1 (leaving only 5 and 8)

Chain Reaction:

  • Looking at the middle block, this leaves you with 6 as a hidden single in F1 and 3 as a hidden single in D2
  • By identifying the hidden pair, you were able to find the answer for two cells within the block

Example 3: Hidden Pairs in a Column

Setup:

  • Column D contains multiple cells with various candidates
  • Cell D8 has candidates: 3, 4, 8, 9
  • Cell D9 has candidates: 8, 9
  • No other cells in column D have candidates 8 or 9

Analysis:

  • Cells D8 and D9 share candidates 8 and 9
  • Numbers 8 and 9 don't appear in any other cells in column D
  • This forms a hidden pair (8, 9)

Elimination:

  • Remove candidates 3 and 4 from D8 (leaving only 8 and 9)

Chain Reactions:

  • This allows you to find a naked pair (3, 4) in D2 and D3
  • The naked pair (3, 4) helps you eliminate the other 3 and 4 candidates in the top center 3×3 block
  • You also discover a hidden single (2) in D1

How Hidden Pairs Work

The Logic Behind Hidden Pairs

The logic is straightforward: if two numbers can only appear in two specific cells within a unit, then those two cells must contain those two numbers (one in each cell). Therefore, all other candidates in those two cells can be eliminated.

Why this works:

  • Each unit (row, column, block) must contain numbers 1-9 exactly once
  • If two numbers can only go in two cells, those cells must contain those numbers
  • Since the cells must contain those numbers, other candidates are impossible

Difference from Naked Pairs

Naked Pairs:

  • Two cells have exactly the same two candidates and no others
  • Obvious because cells have only two candidates
  • Easy to spot visually

Hidden Pairs:

  • Two cells share two candidates, but may have other candidates too
  • Hidden because cells have multiple candidates
  • Requires deeper analysis to discover

Both are powerful: Both techniques eliminate candidates, but hidden pairs are often harder to spot because they're "hidden" among other candidates.

When to Look for Hidden Pairs

Hidden pairs are most useful in these situations:

  • Intermediate to hard puzzles: When basic techniques like singles and naked pairs are insufficient
  • Many pencil marks: When cells have multiple candidates marked
  • Stuck situations: When other techniques aren't providing progress
  • After naked pairs: Naked triples and naked quads often contain hidden pairs, so scan the whole unit and look closely at cells that contain multiple candidates
  • Chain reaction opportunities: When you need to create eliminations that lead to further progress

Common Mistakes When Using Hidden Pairs

Mistake 1: Not Checking All Units

Error: Only looking in rows or only in columns.

Correction: Scan all units systematically—rows, columns, and blocks. Hidden pairs can appear in any unit type.

Mistake 2: Missing Other Occurrences

Error: Not verifying that the two numbers don't appear elsewhere in the unit.

Correction: Always check that the two candidate numbers don't appear in any other cells in that unit. If they do, it's not a hidden pair.

Mistake 3: Wrong Number of Shared Candidates

Error: Using cells that share only one candidate or more than two.

Correction: Hidden pairs require exactly two cells sharing exactly two candidate numbers. If they share one or three or more, it's not a hidden pair.

Mistake 4: Eliminating from Wrong Cells

Error: Eliminating candidates from cells outside the hidden pair.

Correction: Only eliminate other candidates from the two cells that form the hidden pair. Don't eliminate from other cells in the unit.

Mistake 5: Not Using Complete Pencil Marks

Error: Trying to find hidden pairs without complete candidate information.

Correction: Complete pencil marks are essential. You need to see all possible candidates to identify hidden pairs accurately.

Tips for Finding Hidden Pairs

Tip 1: Complete Pencil Marks First

Hidden pairs require complete candidate information. Make sure all possible candidates are marked before looking for hidden pairs.

Tip 2: Scan Systematically

Work through each unit (row, column, block) systematically. Don't skip units or scan randomly.

Tip 3: Look for Shared Candidates

When scanning a unit, look for cells that share candidate numbers. This is the first step to identifying hidden pairs.

Tip 4: Check Naked Triples and Quads

Naked triples and naked quads often contain hidden pairs. When you find these patterns, look closely at the cells involved—they may contain hidden pairs.

Tip 5: Verify Uniqueness

Always verify that the two candidate numbers don't appear in any other cells in that unit. This is critical for confirming a hidden pair.

Tip 6: Look for Chain Reactions

After finding a hidden pair, check how it affects other cells. Hidden pairs often create chain reactions that lead to additional eliminations and placements.

How Hidden Pairs Relate to Other Techniques

Hidden pairs are part of a family of set-based elimination techniques:

  • Naked Pairs: Two cells with exactly the same two candidates (obvious)
  • Hidden Pairs: Two cells sharing two candidates that don't appear elsewhere (hidden)
  • Naked Triples: Three cells with exactly the same three candidates
  • Hidden Triples: Three cells sharing three candidates that don't appear elsewhere
  • Naked Quads: Four cells with exactly the same four candidates
  • Hidden Quads: Four cells sharing four candidates that don't appear elsewhere

Understanding hidden pairs helps you recognize hidden triples and hidden quads, which follow similar logic but with more cells and candidates.

Summary

Hidden pairs occur when two cells within the same row, column, or 3×3 block share two candidate numbers that no other cells contain. The two cells with this hidden set of numbers may contain other candidate numbers, which is why they're considered hidden. You can eliminate all other candidate numbers within these cells because logically the cells have to contain one of the two options in the hidden pair.

To find hidden pairs, use candidate mode to note all possible candidates, scan each unit for two cells with the same two candidate numbers, and ensure these numbers don't appear in any other cell within that unit. Once identified, eliminate all other candidates from those two cells.

Hidden pairs are great for both beginners learning how to play and advanced players leveraging equivalence-based techniques. Finding hidden pairs helps you eliminate candidates and solve your Sudoku puzzle more quickly, often creating chain reactions that allow you to find answers and eliminate numbers elsewhere in the puzzles.

Common mistakes include not checking all units, missing other occurrences, wrong number of shared candidates, eliminating from wrong cells, and not using complete pencil marks. By mastering hidden pair identification and application, you can significantly improve your solving ability, especially in intermediate and hard Sudoku puzzles.

Looking for hidden pairs is a great way to level up your Sudoku skills and solve intermediate or hard Sudoku puzzles. Once you're comfortable with hidden pairs, you can easily add hidden triples to your solving skillset.

Ready to master Hidden Pairs? Try our Sudoku game, learn more techniques, or practice with expert puzzles to develop your pattern recognition skills!

❓ FAQ

Q1: What are hidden pairs in Sudoku?

Hidden pairs occur when two cells within the same row, column, or 3×3 block share exactly two candidate numbers that no other cells in that unit contain. The two cells may contain other candidates (making them "hidden"), but the shared two numbers must be the only two numbers that can appear in those positions.

Q2: How do I find hidden pairs?

To find hidden pairs: use candidate mode to note all possible candidates in each cell, scan each unit (row, column, block) systematically for two cells that share candidate numbers, check if they share exactly two candidate numbers, verify that these two numbers don't appear in any other cells in that unit, then eliminate all other candidates from those two cells.

Q3: What's the difference between naked pairs and hidden pairs?

Naked pairs consist of two cells in the same unit that have exactly the same two candidates and no others (obvious). Hidden pairs consist of two cells that share two candidate numbers that don't appear elsewhere in that unit, but the cells may have other candidates too (hidden). Both eliminate candidates, but hidden pairs are harder to spot.

Q4: Can hidden pairs appear in rows, columns, and blocks?

Yes, hidden pairs can appear in any unit type: rows, columns, or 3×3 blocks. The key requirement is that both cells must be in the same unit and share exactly two candidate numbers that don't appear elsewhere in that unit.

Q5: What should I do after finding a hidden pair?

After finding a hidden pair, eliminate all other candidates from those two cells (except the two numbers in the hidden pair). Then check for chain reactions—hidden pairs often lead to additional eliminations and placements, sometimes revealing hidden singles or creating opportunities for other techniques.

Q6: Do I need complete pencil marks to find hidden pairs?

Yes, complete pencil marks are essential for finding hidden pairs. You need to see all possible candidates in each cell to identify which cells share candidate numbers and verify that those numbers don't appear elsewhere in the unit.

Q7: Can hidden pairs create chain reactions?

Yes, hidden pairs often create chain reactions. After eliminating other candidates from the two cells, you may discover hidden singles, naked pairs, or opportunities for locked candidate techniques. The example with column D showed how a hidden pair led to a naked pair and a hidden single.

Q8: When should I look for hidden pairs?

Look for hidden pairs in intermediate to hard puzzles when basic techniques are insufficient, when puzzles have many pencil marks, when you're stuck and other techniques aren't providing progress, after finding naked triples/quads (which often contain hidden pairs), or when you need to create eliminations that lead to further progress.

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