Hidden Pairs: The Art of Uncovering Logic
The Concept
A Hidden Pair occurs when two specific candidates appear in only two cells within a house (Row, Column, or Box), even though those cells may contain other "noise" candidates.
Unlike Naked Pairs (where the cells clearly contain only two numbers), Hidden Pairs are buried. The logic, however, is undeniable: because these two numbers cannot go anywhere else in the group, they must belong to these two specific cells.
The Logic Rule
If, within a specific House (e.g., Column 8):
- Candidate 4 appears only in Cell A and Cell B.
- Candidate 7 appears only in Cell A and Cell B.
Then: You can safely eliminate all OTHER candidates (the noise) from Cell A and Cell B.
Result: These cells become a clean Naked Pair {4, 7}.
Detection Methods
Hidden pairs are notoriously difficult to spot because you aren't looking for cells that look alike; you are looking for candidates that behave alike.
1. Cross-Hatching (The Efficient Way)
This is the most common way to stumble upon hidden pairs while using Snyder Notation.
- Process: You focus on the number 4 and realize it is restricted to only two spots in Column 8 (Rows 4 and 5). You mark them.
- The "Aha" Moment: Later, you focus on the number 7. You realize it is restricted to the exact same two spots in that column.
- Conclusion: Even if other numbers (like 3 or 6) are currently penciled into those spots, the 4 and 7 must live there. They push the other numbers out.
2. Candidate Distribution (The Thorough Way)
- Process: Scan a specific house (like Column 8) number by number.
- Ask: "Where can the 4 go?" (Positions 4 and 5). "Where can the 7 go?" (Positions 4 and 5).
- Match: Since 4 and 7 share the exact same limited availability, they form a Hidden Pair.
Practical Example: From Hidden to Naked
Let's look closely at Column 8 in the image above.
Phase 1: Analysis
- Look at R4C8: It contains {4, 6, 7}.
- Look at R5C8: It contains {3, 4, 7}.
- At first glance, they don't look related. But if you scan the whole column, you will see that 4 and 7 do not exist anywhere else. They are "hiding" in these two cells.
Phase 2: The Cleanup (Internal Elimination)
Because 4 and 7 must claim these spots, the other numbers are invalid.
- Remove the 6 from R4C8.
- Remove the 3 from R5C8.
- Status: We now have a clean Naked Pair {4, 7}.
Phase 3: The Consequence (Naked Pair, External Elimination)
Now that R4C8 and R5C8 are "locked" as {4, 7}:
- We look at the rest of Column 8.
- We see R2C8 contains {2, 4}.
- Since the 4 is now locked in rows 4 & 5, we eliminate the 4 from R2C8.
- Result: R2C8 becomes a 2 (Naked Single). Solved!
Strategy Tips
- Inverse Relationship: Hidden Pairs are the strategic inverse of Naked Pairs.
- Naked: Candidates are limited to the cells → Eliminate from neighbors.
- Hidden: Candidates are limited by the house → Eliminate from the cells themselves.
- Trust the Notation: If you use Corner marks on Minimal Sudoku, Hidden Pairs often reveal themselves as two corners sharing the exact same two dots.
- Don't Force It: If you are stuck, switch from scanning "cells" (what is inside this box?) to scanning "numbers" (where can the number 4 go?).
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