Hidden Pairs in Sudoku: The Complete Guide

What is a Hidden Pair?

A hidden pair occurs when two candidates appear in exactly two cells within a unit (row, column, or box), but those cells also contain other candidates. The pair is "hidden" among other numbers.

Example:

Imagine a row where the numbers 3 and 7 only appear as candidates in cells 4 and 6. Cell 4 has candidates {2, 3, 5, 7}, and cell 6 has candidates {3, 6, 7, 9}. Since 3 and 7 can only go in these two cells, they form a hidden pair. You can eliminate 2, 5 from cell 4 and 6, 9 from cell 6, leaving {3, 7} in both cells.

Why Hidden Pairs Matter

They unlock progress in intermediate puzzles where basic techniques fail.
They reduce candidates in cells that seem complicated.
They often reveal naked singles after elimination.
They teach pattern recognition skills needed for advanced techniques.

How to Spot a Hidden Pair

Scan a unit systematically.
Pick a row, column, or box. Look at where each candidate number (1-9) appears.
Identify two numbers that appear in exactly two cells.
For example, if 4 and 8 only appear in cells A and B within that unit, you've found a potential hidden pair.
Check if those cells contain other candidates.
If cell A has {4, 8} only, it's a naked pair, not hidden. But if cell A has {2, 4, 5, 8} and cell B has {4, 6, 8}, the pair is hidden.
Eliminate all other candidates from those cells.
Remove 2, 5 from cell A and 6 from cell B, leaving only {4, 8} in both cells.

Hidden Pair vs Naked Pair

These complementary techniques are often confused:

Naked pair: Two cells contain exactly the same two candidates {X, Y}, and you eliminate X and Y from other cells in the unit.
Hidden pair: Two candidates X and Y appear in only two cells (which may have additional candidates), and you eliminate other candidates from those two cells.

Think of it this way: naked pairs eliminate outward (affect other cells), while hidden pairs eliminate inward (clean up the pair cells themselves).

Step-by-Step Example

Let's examine a practical scenario in Row 5:

Row 5 candidates:

Cell 1: {1, 4, 9}
Cell 2: {1, 4, 9}
Cell 3: {2, 5, 8}
Cell 4: {2, 5, 6, 8}
Cell 5: [filled]
Cell 6: {2, 6, 8}
Cell 7: {2, 6, 8}
Cell 8: [filled]
Cell 9: {1, 4, 9}

Analysis: Look at where 5 appears—only in cells 3 and 4. Now check where 6 appears—only in cells 4, 6, and 7. Wait, that's three cells, not two.

Let's try again: Where does 5 appear? Cells 3 and 4 only. Where does 8 appear? Cells 3, 4, 6, and 7. That's too many.

Actually, look closer at 5 and 6: If 5 only appears in cells 3 and 4, and within those same cells... wait, 6 appears in cell 4 but also cells 6 and 7.

Let me reconsider with 2 and 5: Where does 2 appear? Cells 3, 4, 6, 7. Where does 5 appear? Only cells 3 and 4.

Correct identification: Numbers 5 appears only in cells 3 and 4. Looking systematically, if we find another number that also appears in only those same two cells, we have a hidden pair. In this case, checking all candidates, we notice this isn't a perfect example—let me provide a clearer one.

Clearer Example:

Box 7 (bottom-left 3×3 box) candidates:

Cell A: {3, 5, 7, 9}
Cell B: {2, 4, 6, 8}
Cell C: {2, 4, 6, 8}
Cell D: {1, 3, 5, 7, 9}
Cell E: [filled]
Cell F: {2, 4, 6, 8}
Cell G: {3, 5, 7, 9}
Cell H: {2, 4, 6, 8}
Cell I: [filled]

Analysis: Where does 1 appear in this box? Only in cell D. That's a hidden single, not a pair.

Where does 3 appear? Cells A, D, and G. Where does 5 appear? Cells A, D, and G. Where does 7 appear? Cells A, D, and G. Where does 9 appear? Also cells A, D, and G.

Now check the even numbers: Where does 2 appear? Cells B, C, F, H. Where does 4 appear? Cells B, C, F, H. Where does 6 appear? Cells B, C, F, H. Where does 8 appear? Cells B, C, F, H.

Wait—look at this pattern! Numbers 2, 4, 6, and 8 all appear in the same four cells (B, C, F, H). This is actually a hidden quad, not a hidden pair. But the principle is the same: these four numbers can only go in these four cells, so we can eliminate any other candidates from those cells.

Simple Hidden Pair Example:

Column 3 candidates:

Row 1: {2, 7, 8}
Row 2: {2, 7, 8, 9}
Row 3: [filled]
Row 4: {4, 5}
Row 5: {4, 5, 6}
Row 6: [filled]
Row 7: {2, 7, 9}
Row 8: [filled]
Row 9: [filled]

Analysis: Where does 4 appear in this column? Only rows 4 and 5. Where does 5 appear? Only rows 4 and 5!

Hidden pair found: {4, 5} in rows 4 and 5 of column 3.

Action: Eliminate 6 from row 5, leaving {4, 5} in both cells. Now you have a clean pair that will eventually resolve to one cell being 4 and the other being 5.

Visual Example

Before: Row 8 has cells with candidates {1, 3, 4, 6} and {1, 3, 7, 8}, plus other filled cells.
Observation: Scanning the row, you notice that 4 and 6 only appear in those two specific cells (among others).
Wait, that doesn't work: 4 appears in the first cell only, and 6 appears in the first cell only. Let me reconsider...
Correct scenario: Row 8 has cells with {1, 4, 6, 9} and {1, 4, 6, 8}.
Check: Where does 4 appear in the row? Only these two cells. Where does 6 appear? Only these two cells.
Hidden pair confirmed: {4, 6} is hidden in these cells.
After elimination: Remove 1, 9 from the first cell and 1, 8 from the second cell, leaving {4, 6} in both.
Result: You've cleaned up two messy cells and established a locked pair.

Strategies for Spotting Hidden Pairs Quickly

Systematic unit scanning
Check one unit at a time. For each number 1-9, mark which cells contain it. Look for two numbers that share exactly the same two cells.
Focus on crowded units
Rows, columns, or boxes where most cells have 4-5 candidates are prime hunting grounds for hidden pairs.
Use a candidate matrix
Some solvers create a grid showing which numbers appear where. This makes patterns jump out visually.
Look for complementary patterns
If you see a naked pair in a unit, check if there's a hidden pair among the remaining cells.
Practice with restricted candidates
Numbers that appear in only 2-3 places are easier to track. Start with those when searching for hidden pairs.

Common Pitfalls

Confusing hidden pairs with naked pairs: Remember, hidden pairs require elimination within the pair cells, not from other cells.
Missing the forest for the trees: When cells have many candidates, it's easy to overlook which specific numbers form the pair.
Incomplete elimination: After finding a hidden pair, make sure you remove ALL other candidates from those two cells.
Forgetting to update: After eliminating candidates, new naked singles might appear elsewhere. Don't forget to check!
Looking in wrong units: A hidden pair exists within a single row, column, or box—not across multiple units.

Practice: Find the Hidden Pair

Try this box (3×3 section):

Box 4 (middle-left) candidates:

Cell 1: {1, 8, 9}
Cell 2: {1, 2, 5, 8, 9}
Cell 3: {2, 5, 8}
Cell 4: {3, 7}
Cell 5: [filled with 6]
Cell 6: {2, 3, 5, 7}
Cell 7: {1, 8, 9}
Cell 8: {1, 2, 5, 8, 9}
Cell 9: [filled with 4]

Question: Can you find the hidden pair?

Solution: Look at where 3 appears: cells 4 and 6 only. Look at where 7 appears: cells 4 and 6 only. Hidden pair {3, 7} found!

Action: Cell 4 already has only {3, 7}—perfect. Cell 6 has {2, 3, 5, 7}, so eliminate 2 and 5, leaving {3, 7}.

Why Hidden Pairs Set the Stage

Hidden pairs bridge the gap between basic techniques and advanced pattern recognition. Once you master them, you'll find that:

They prepare you for hidden triples and hidden quads
They sharpen your ability to scan units systematically
They often chain together with other techniques—finding a hidden pair might expose a naked pair, which reveals a naked single
They teach you to think about candidate distribution, which is crucial for advanced moves like X-Wing and Swordfish

Quick Recap

Technique	How it Works	Elimination Direction	Difficulty
Naked Pair	Two cells have exactly two candidates	Outward (other cells)	Intermediate
Hidden Pair	Two candidates appear in only two cells	Inward (pair cells)	Intermediate
Naked Triple	Three cells contain three candidates	Outward (other cells)	Intermediate
Hidden Triple	Three candidates appear in only three cells	Inward (triple cells)	Intermediate

Final Thought

When you're stuck on an intermediate puzzle, ask yourself: have I checked for hidden pairs? They're often lurking in crowded units, waiting to simplify your grid.

Frequently Asked Questions

What is a Hidden Pair in Sudoku?

A hidden pair occurs when two candidates appear in exactly two cells within a unit (row, column, or box), but those cells also contain other candidates. The pair is "hidden" among other numbers. Once identified, you can eliminate all other candidates from those two cells, leaving only the hidden pair.

How do I spot a Hidden Pair?

To spot a hidden pair: 1) Look for two numbers that appear in exactly two cells within a unit, 2) Check if those same two cells contain other candidates (making the pair "hidden"), 3) Eliminate all other candidates from those two cells, leaving only the pair. Focus on rows, columns, or boxes with many candidates penciled in.

What's the difference between Hidden Pairs and Naked Pairs?

Naked pairs have exactly two candidates visible in two cells, and you eliminate those candidates from other cells in the unit. Hidden pairs have two candidates that appear in only two cells, but those cells have additional candidates that must be eliminated. Naked pairs eliminate outward; hidden pairs eliminate inward.

Why are Hidden Pairs important?

Hidden pairs are important because they unlock progress in intermediate puzzles where basic techniques fail, they reduce candidates in cells that seem complicated, they often reveal naked singles after elimination, and they teach pattern recognition skills needed for advanced techniques.

When should I look for Hidden Pairs?

Look for hidden pairs after exhausting naked singles and hidden singles. They're especially useful in crowded rows, columns, or boxes where cells have 4-5 candidates each. Scan systematically: pick a unit, identify which two numbers appear in only two cells, then check if those cells have extra candidates to eliminate.

Ready to advance? Check out our complete strategy guide for more techniques.

Related Strategies

Once you've mastered hidden pairs, these techniques build naturally:

Naked Pairs - The complementary technique that eliminates outward
Hidden Singles - The simpler predecessor to hidden pairs
Hidden Triples - Extension of hidden pairs with three numbers (coming soon)
Naked Triples - Three-cell version of naked pairs (coming soon)
X-Wing - Advanced pattern recognition that builds on pair logic

Practice Hidden Pairs

Next up: Try Pointing Pairs to learn about locked candidates (coming soon).

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