Hidden Pairs Strategy

When two numbers can only go in two specific cells within a unit, all other candidates in those cells can be removed.

Difficulty (Scanning skill)

Intermediate

Cells in pattern (Same unit)

2

Locked digits (Found by scanning)

2

Eliminations (Within the 2 cells)

Inside

What Is a Hidden Pair?

A Hidden Pair exists when two specific candidate numbers within a row, column, or box can only be placed in exactly two cells. Even though these cells may contain additional candidates, the two "hidden" numbers are locked into those cells - meaning all other candidates in those two cells can be safely removed.

For example, suppose in a particular row, the numbers 2 and 8 only appear as candidates in cells C3 and C7. Even if C3 has candidates [2, 5, 8, 9] and C7 has candidates [1, 2, 8], the 2 and 8 form a Hidden Pair. You can eliminate 5 and 9 from C3, and 1 from C7, leaving both cells with just [2, 8].

After this reduction, the Hidden Pair effectively becomes a Naked Pair, and you can then eliminate 2 and 8 from other cells in any additional shared units. See more terminology in our Sudoku glossary.

How to Find Hidden Pairs: Step-by-Step

1. Ensure complete pencil marks - Accurate candidate notation is critical. Every empty cell should have all valid candidates listed. Hidden Pairs are nearly impossible to find without this foundation.
2. Choose a unit to analyze - Select a row, column, or box. Units with moderate numbers of empty cells (3-5) are the best hunting grounds for Hidden Pairs.
3. Count where each number appears - For each candidate number in the unit, note how many cells contain it. You are looking for numbers that appear as candidates in exactly two cells.
4. Look for matching pairs of numbers - If two different numbers both appear in exactly the same two cells within the unit, you have found a Hidden Pair. The two numbers are locked into those two cells.
5. Eliminate extra candidates - Remove all candidates other than the pair numbers from the two cells. Then check for new singles or further patterns in the simplified grid.

When to Use Hidden Pairs

Hidden Pairs are most useful when you have already exhausted singles and Naked Pairs without fully solving the puzzle. They are a staple technique for medium and hard Sudoku puzzles.

The elimination from Hidden Pairs is different from Naked Pairs: instead of removing the pair candidates from other cells, you remove non-pair candidates from the pair cells themselves. This simplification often leads to further discoveries. Check our strategies overview for the full solving hierarchy, or start from how to play Sudoku.

Difficulty Level & Puzzle Types

Hidden Pairs is classified as an intermediate-level technique. It requires more analytical thinking than Naked Pairs because you must examine candidate distributions across an entire unit rather than individual cells.

Easy

Rarely needed - singles handle most eliminations

Medium

Occasionally needed - supplements Naked Pairs

Hard

Frequently useful - a key intermediate technique

Expert

Part of the solving arsenal alongside advanced methods

Tips for Mastering Hidden Pairs

1. Create a frequency table: for each unit, count how many cells contain each candidate number. Numbers appearing exactly twice are your primary targets.
2. Focus on units where many candidates are clustered in a few cells - these dense cells are where Hidden Pairs tend to hide.
3. After stripping extra candidates from Hidden Pair cells, the pair effectively becomes a Naked Pair. Use this to make further eliminations in shared units.
4. Practice alongside Hidden Triples to develop a strong eye for candidate distribution patterns.

Frequently Asked Questions

What is a Hidden Pair in Sudoku?

A Hidden Pair occurs when two candidate numbers can only appear in exactly two cells within a row, column, or 3x3 box. Those two cells may contain other candidates as well, but since the pair of numbers is restricted to those cells, all other candidates can be removed from them.

How is a Hidden Pair different from a Naked Pair?

In a Naked Pair, two cells contain ONLY two candidates (e.g., both have {3,7}). In a Hidden Pair, the two cells may have additional candidates, but a specific pair of numbers only appears in those two cells within the unit. The Hidden Pair lets you remove the extra candidates from those cells.

Why are Hidden Pairs harder to find than Naked Pairs?

Hidden Pairs require you to analyze where specific numbers can go within a unit, rather than just looking at individual cells. The pair is 'hidden' among other candidates, making it less visually obvious. With practice and good pencil marks, they become easier to spot.

Can a Hidden Pair exist in more than one unit simultaneously?

Yes, the same two cells might form a Hidden Pair in both a row and a box (for example), if the two numbers are restricted to those cells in both units. This can result in additional eliminations from the second unit.

What should I do after finding a Hidden Pair?

Remove all candidates other than the pair numbers from the two cells. Then re-scan the affected unit for new Naked Singles, Hidden Singles, or other patterns that the simplification may have revealed.

Related Techniques

• Naked Pair vs Hidden Pair - Two faces of the same logic
• Naked Pairs - Two cells with exactly the same two candidates
• Hidden Triples - Three numbers limited to three cells in a unit
• Hidden Singles - A number with only one possible placement in a unit
• Pointing Pairs - Box candidates restricted to a single row or column

Related Glossary Terms

• Naked Pair
• Candidate
• Cell
• Elimination
• House

View full glossary

Practice by Difficulty

• Easy Sudoku - Solving guide
• Medium Sudoku - Solving guide
• Hard Sudoku - Solving guide
• Expert Sudoku - Solving guide

See it in action: a Hidden Pair

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In row 1, where can the digit 5 go? Look across all the empty cells.

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