What are naked pairs in Sudoku?
A naked pair is one of the most useful intermediate Sudoku techniques. Once you have pencil marks in place, naked pairs reveal themselves clearly and can cascade into multiple placements.
What Is a Naked Pair?
A naked pair occurs when exactly two cells in the same row, column, or 3×3 box each contain exactly the same two candidates and no others. For example if cells R3C2 and R3C7 both contain only {4, 7}, then 4 and 7 must fill those two cells in some order. No other cell in row 3 can contain 4 or 7 - Remove them from all other cells in that row.
Step-by-Step Example
A box has these candidates remaining:
- Cell A: {2, 8}
- Cell B: {2, 8}
- Cell C: {2, 5, 8}
- Cell D: {3, 5}
Cells A and B form a naked pair on {2, 8}. Remove 2 and 8 from Cell C. Cell C is now {5} - A naked single. Place 5. Cell D was {3, 5} and now loses the 5, becoming {3} - Another naked single. One naked pair cascaded into two immediate placements.
Naked Triples and Quads
The same logic extends upward. A naked triple is three cells in a unit where the union of all their candidates contains exactly three digits. Those digits must fill those three cells - Remove them from all other cells in the unit. A naked quad works the same way with four cells and four candidates. Quads are rare but do appear in Expert and harder puzzles.
Naked Pairs vs Hidden Pairs
A hidden pair is the complement: two digits that can only appear in the same two cells within a unit, even though those cells have other candidates too. You identify them by scanning for digits restricted to just two cells in a unit, then clear all other candidates from those two cells. Both techniques achieve candidate reduction but you find them in opposite ways.