Naked pairs are one of the first intermediate techniques every serious Sudoku solver should master.
What Are Naked Pairs?
A naked pair is a powerful Sudoku technique that allows you to eliminate candidates from cells. It occurs when two cells in the same row, column, or 3×3 box each contain exactly the same two candidates — and no others.
When this happens, you know those two digits will fill those two cells (in some order), which means no other cell in that row, column, or box can contain either of those digits.
Why "Naked"?
The term "naked" refers to the fact that these candidates are fully visible in their cells — there's no hidden information. You can see the pair directly in the candidate lists.
A Simple Example
Suppose in a particular row, two cells both show candidates {4, 7}:
Since one of these cells must contain 4 and the other must contain 7, no other cell in that row can hold a 4 or a 7. You can safely eliminate 4 and 7 from all other candidates in the row.
Why This Works
Think about it logically: Cell A must be either 4 or 7. Cell B must be the other one. There's no scenario where 4 or 7 appears in any other cell in the row — those two "slots" for 4 and 7 are completely occupied by these two cells.
Step-by-Step Method
Step 1: For every row, column, and box, list out all cells and their candidates.
Step 2: Look for two cells in the same house (row, column, or box) that contain exactly the same two candidates.
Step 3: Once found, eliminate both of those candidates from all other cells in the shared house.
Step 4: Check if any eliminations created new naked singles or hidden singles.
Extended Family: Naked Triples and Quads
The naked pair concept extends naturally:
Naked Triple — Three cells in the same house containing exactly the same three candidates (e.g., all three cells have candidates from {2, 5, 9}). Eliminate 2, 5, and 9 from all other cells in the house.
Naked Quad — Four cells sharing exactly four candidates. Rarer, but very powerful when it occurs.
Note: For triples and quads, each individual cell doesn't need all three/four candidates — just that the union of candidates across all cells in the group equals exactly three/four digits.
Naked Pairs vs Hidden Pairs
People often confuse naked pairs with hidden pairs. The difference:
Both are powerful, but naked pairs are usually easier to spot visually.
Real Puzzle Application
Consider a 3×3 box with these candidate arrangements:
Spot the naked pair? R1C2 = {2,5} and R2C2 = {2,5}. Both cells share the same column (C2). Eliminate 2 and 5 from all other cells in column 2. This affects any other cell in column 2 throughout the whole grid.
Tips for Finding Naked Pairs Quickly
When to Use Naked Pairs
Naked pairs are typically useful after:
They bridge the gap between beginner techniques and more advanced methods like X-Wing or Swordfish.
Conclusion
Naked pairs are a cornerstone technique of serious Sudoku solving. They're logical, satisfying to find, and often unlock significant portions of a puzzle. Master this technique and you'll be well on your way to tackling hard and expert-level Sudoku puzzles with confidence.