Hidden Pairs
Hidden pairs are the complement to naked pairs. They're "hidden" because the cells contain other candidates that obscure the pattern. Once you find them, they become powerful elimination tools.
What is a Hidden Pair?
A hidden pair occurs when two candidates appear in exactly two cells within a unit, even if those cells contain other candidates.
Example: If 4 and 9 only appear in cells A and B of a row (among their various candidates), that's a hidden pair.
The pair is "hidden" because other candidates in those cells mask the pattern.
Visual Example
Before elimination:
What's happening:
- Look at where 4 can go in this row: only cells A and B
- Look at where 9 can go in this row: only cells A and B
- Both numbers are "locked" to these same two cells
After elimination:
The hidden pair [4,9] becomes a visible naked pair [4,9].
The Logic Explained
Think about it step by step:
- The 4 must go somewhere in this row
- The only cells that can have 4 are A and B
- The 9 must also go somewhere in this row
- The only cells that can have 9 are A and B
- So one cell gets 4, the other gets 9
- This means A and B can ONLY contain 4 or 9
The result: Remove all other candidates from cells A and B!
Hidden Pairs vs. Naked Pairs
| Aspect | Naked Pair | Hidden Pair |
|---|---|---|
| Definition | Two cells with ONLY two candidates | Two candidates in ONLY two cells |
| Extra candidates | Not allowed | Allowed (they hide the pattern) |
| Elimination | Remove pair digits from OTHER cells | Remove OTHER digits from PAIR cells |
| Visibility | Easy to spot | Harder to spot |
Both are equally powerful — they're just found differently!
How to Find Hidden Pairs
Method 1: Candidate Mapping
- Pick a unit (row, column, or box)
- For each number 1-9, list which cells can hold it
- Find two numbers that share exactly the same two cells
- That's your hidden pair!
Example mapping for a row:
- 1: cells C, E, F, G
- 2: cells C, E, F, G
- 3: (already placed)
- 4: cells A, B ← only 2 cells!
- 5: cells B, C, F
- 6: cells A, C
- 7: (already placed)
- 8: cells E, F, G
- 9: cells A, B ← same 2 cells as 4!
Found it! 4 and 9 both appear only in cells A and B.
Method 2: Look for Rare Candidates
- Focus on candidates that appear in few cells
- Digits appearing in only 2 cells are most likely to form pairs
- Check if any two such digits share the same cells
Method 3: Process of Elimination
After finding and applying naked pairs:
- Re-examine the remaining candidates
- Hidden pairs often emerge after eliminations
- Keep checking as the puzzle progresses
Hidden Pairs in Boxes
Boxes are great places to find hidden pairs:
After elimination:
Double Duty
When a hidden pair is found, you get two benefits:
- Elimination: Remove other candidates from the pair cells
- Transformation: The hidden pair becomes a naked pair
The new naked pair might create more eliminations in the same unit!
Step-by-Step Finding Process
Let's walk through finding a hidden pair:
Given this row:
Step 1: Map each digit
- 1: A, C, E, I
- 2: B, C, G
- 3: A, E, H, I
- 5: A, C, E
- 6: A, B, G, H
- 8: B, E, G
- 9: B, C, H, I
Step 2: Look for matching pairs
- Check digits appearing in only 2 cells
- None here appear in exactly 2 cells
Step 3: Check digit combinations
- 2 and 8 both include B, G — but 2 also has C, and 8 also has E
- Not a pair
No hidden pair in this row. That's okay — not every unit has one!
When Hidden Pairs Are Most Useful
Hidden pairs shine when:
- A unit has many candidates spread around
- You can't find naked pairs
- Cells have 4+ candidates (hiding the pair)
- You've exhausted simpler techniques
Practice Exercises
Exercise 1: Find the hidden pair
Hint
Look at where each digit can go. Which two digits share the same two cells?
Answer
Hidden pair on 4, 5!
Map the digits:
- 1: cells A, C, E, G, I
- 2: cells A, E, F, G, H, I
- 3: cells A, E
- 4: cells C, F only ← only 2 cells!
- 5: cells C, F only ← only 2 cells!
- 7: cells A, E, G, H
- 8: cells C, F
Both 4 and 5 appear only in cells C and F. That's a hidden pair!
Elimination: Remove all other candidates from C and F:
- C: [1,4,5,8] → [4,5]
- F: [2,4,5,8] → [4,5]
Now C and F form a naked pair [4,5], which eliminates 4 and 5 from other cells in the row.
Exercise 2: Find the hidden pair in this box
Answer
Hidden pair on 8, 9!
Map the digits:
- 1: cells A, B, H, I
- 2: cells A, E, H, I
- 3: cells A, B, E, I
- 4: cells A, E, I
- 8: cells B, G only ← only 2 cells!
- 9: cells B, G only ← only 2 cells!
Both 8 and 9 appear only in cells B and G. That's a hidden pair!
Elimination: Remove all other candidates from B and G:
- B: [1,3,8,9] → [8,9]
- G: [8,9] → already clean!
Cell B is cleaned up. The hidden pair becomes a naked pair [8,9].
Common Mistakes
Mistake 1: Wrong elimination direction
- Hidden pair: eliminate OTHER candidates FROM the pair cells
- NOT: eliminate pair candidates from OTHER cells
- That's what naked pairs do!
Mistake 2: Incomplete digit mapping
If you miss that a digit appears in a 3rd cell, you'll falsely identify a pair. Always double-check.
Mistake 3: Stopping after finding the pair
After cleaning up a hidden pair, it becomes a naked pair. Apply the naked pair eliminations too!
Mistake 4: Confusing frequency
- Hidden pair: two digits in exactly two cells
- NOT: two cells with only two digits (that's a naked pair)
Mistake 5: Forgetting to verify
Before eliminating, verify:
- Both digits appear in ONLY these two cells
- No other cell in the unit has either digit
Quick Reference
Hidden pair definition:
- Two candidates appearing in exactly two cells
- Those cells may have other candidates
- Other candidates are eliminated from the pair cells
Finding hidden pairs:
- Map each digit to its possible cells
- Look for two digits sharing exactly two cells
- Verify no other cells have those digits
Elimination rule:
- Remove non-pair candidates from pair cells
- NOT: remove pair candidates from other cells
When to look:
- Medium to Expert puzzles
- After basic techniques stall
- When cells have many candidates
What's Next?
Once you master hidden pairs:
- Hidden Triples — Three candidates in only three cells
- Hidden Quads — Four candidates in only four cells
- X-Wing — Cross-row/column elimination pattern