Naked Pairs: The Essential Elimination Strategy
The Concept
A Naked Pair describes a state where two cells in the same house (Row, Column, or Box) contain identical candidate lists of exactly two numbers.
Because these two cells must eventually contain those two specific numbers, those numbers are "locked" into those positions. Consequently, no other cell in that house can contain those numbers.
This is an elimination strategy. It rarely solves a cell immediately but clears "noise" from the grid to reveal hidden singles.
The Logic Rule
If Cell A and Cell B are in the same house, and:
- Cell A contains only candidates {x, y}
- Cell B contains only candidates {x, y}
Then: You can safely remove x and y from the pencil marks of all other cells in that house.
Detection Methods
On Minimal Sudoku, you can spot these pairs using two different notation styles.
1. Scanning Candidate Lists (Center Notes)
Best for: Complex, end-game puzzles.
If you use full candidate notation (filling every possible number), look for two cells in a group that look visually identical, containing only two numbers.
- Signal: You scan Row 2 and see two cells reading "4,9" and "4,9".
- Action: Scan the rest of Row 2 (and the Box they sit in) and erase every other "4" and "9".
2. Snyder Notation (Corner Notes)
Best for: Speed solving and clean grids.
Snyder Notation focuses on restricting candidates to specific cells.
- Signal: You notice that candidates 4 and 9 are both restricted to the same two cells (e.g., the top-left corners) within a 3x3 box.
- Action: Even if you haven't marked the center notes yet, you know these two cells form a pair. No other numbers can exist in these two spots.
Practical Example: Dual House Elimination
In the image above, we see a powerful setup involving Row 2.
Analysis:
- Identify: The first two cells (Row 2, Column 1 & 2) contain only the candidates 4 and 9.
- Verify: These cells share two houses: they are in the same Row (Row 2) AND the same Box (Box 1).
- Eliminate:
- In the Row: Remove 4 and 9 from the rest of Row 2. (e.g., R2C3 changes from {1, 4, 9} to a solved {1}).
- In the Box: Remove 4 and 9 from any other cells inside Box 1.
Note: This specific alignment is highly valuable because it clears candidates from two distinct groups simultaneously.
Strategy Tips
- House Overlap: As seen in the example, pairs are most powerful when they sit in an intersection (sharing both a Row and a Box). Always check both directions!
- Naked vs. Hidden: A "Naked" pair implies the cells only have those two numbers. If the numbers are buried among others (e.g. {1,2,3} and {1,2,4}), look for Hidden Pairs instead.
- Triples: This logic scales. If you find three cells sharing the same three candidates (e.g., {1,2}, {2,3}, {1,3}), you have found a Naked Triple.
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