What is a Naked Single?
A Naked Single is the most fundamental and straightforward technique in Sudoku. It occurs when a cell has only one possible candidate remaining after all other numbers have been eliminated by the rules of Sudoku. When you find a Naked Single, you can fill in that number with absolute certainty.
The term "naked" refers to the fact that this single candidate stands alone – there are no other possibilities hiding in that cell. It's completely exposed and obvious once you spot it!
The Core Concept
Every cell in Sudoku must contain exactly one number from 1 to 9. A Naked Single emerges through the process of elimination: by examining the row, column, and 3×3 box that contain a cell, we can rule out numbers that already appear in those units. When only one number remains possible, we've found a Naked Single.
How to Find Naked Singles
Step-by-Step Process:
- Choose an empty cell to analyse
- Check its row – note all numbers already present (1-9)
- Check its column – note all numbers already present
- Check its 3×3 box – note all numbers already present
- Identify what's left – list the numbers NOT present in row, column, or box
- If only one number remains – you've found a Naked Single! Fill it in.
- If multiple numbers remain – this cell is not a Naked Single (yet). Note the candidates and move on.
Visual Example
Only 8 is possible!
When all other numbers (1-7, 9) are eliminated by surrounding cells, only 8 remains – that's a Naked Single.
Analysing the Example
Understanding the Puzzle
In the displayed image, we can observe several important elements that demonstrate how Naked Singles work in practice:
The Blue Cell (Row 3, Column 4): The prominent blue-highlighted 8 represents a Naked Single that has been identified. This cell could only contain the number 8 after eliminating all other possibilities based on the numbers already present in its row, column, and 3×3 box.
Red Circled Numbers: The various numbers marked with red circles (such as 4, 3, 7, 6, 1, 2, 9, and others) indicate candidates or numbers that are part of the analysis process. These might represent:
- Numbers being tracked during the elimination process
- Potential Naked Singles that need verification
- Numbers that constrain what can go in nearby empty cells
Green Cells: The cells with green backgrounds containing 8s show how the placement of one Naked Single can influence and confirm other placements in the grid. Once the blue 8 is placed, it helps confirm or eliminate possibilities in related cells.
How the Blue 8 Was Found
To identify that cell as a Naked Single containing 8, the solver would have:
- Examined row 3 and noted which numbers were already present
- Examined column 4 and noted the existing numbers
- Examined the top-middle 3×3 box and noted its numbers
- Combined all three constraints to find that only 8 could fit in that position
- Confidently placed 8 in the blue-highlighted cell
Why Naked Singles Matter
The Foundation of All Sudoku Solving
Naked Singles are not just the easiest technique – they're the most important one. Here's why:
- Starting point: Most puzzles begin with Naked Singles in the grid
- Chain reaction: Finding one Naked Single often reveals several more
- Validation: They confirm that your previous moves were correct
- Breakthrough: Advanced techniques often create Naked Singles as their end result
- Universal: Even in the hardest puzzles, Naked Singles eventually appear
The Naked Single Cascade
One of the most satisfying aspects of Sudoku is the "cascade effect" that Naked Singles create. When you fill in a Naked Single, it eliminates that number as a possibility from all cells in the same row, column, and box. This elimination often creates new Naked Singles, which create more Naked Singles, and so on.
Example of a Cascade:
- You find that cell A1 must be 5 (Naked Single)
- Placing 5 in A1 means 5 is eliminated from all of row A, column 1, and the top-left box
- Cell A8, which previously had candidates {5, 7}, now only has {7} – a new Naked Single!
- Placing 7 in A8 eliminates 7 from row A, column 8, and the top-right box
- This creates yet another Naked Single in cell B9...
This domino effect can solve large portions of easier puzzles in rapid succession.
Pencil Marks and Naked Singles
Many solvers use "pencil marks" (also called "candidates") to track possibilities in each empty cell. Pencil marks make finding Naked Singles much easier:
- Full notation: Write all possible candidates (1-9) in each empty cell, then eliminate based on constraints
- Scan for singles: Cells with only one pencil mark are Naked Singles
- Update after placements: When you fill a number, erase it from all related pencil marks
- Visual clarity: Naked Singles "pop out" when properly marked
Common Mistakes to Avoid
- Missing a constraint: Always check all three units (row, column, AND box) before concluding a number is possible
- Incorrect elimination: Double-check that you've correctly identified which numbers are already present
- Assuming without checking: Never guess – always verify that only one number is truly possible
- Ignoring cascades: After placing a Naked Single, immediately look for new ones nearby
- Skipping pencil marks: In complex positions, trying to track everything mentally leads to errors
When Naked Singles Aren't Enough
In easier Sudoku puzzles, you can solve the entire grid using only Naked Singles (and their close cousin, Hidden Singles). However, as puzzles become more difficult, you'll eventually reach a point where no Naked Singles exist.
This is when you need to employ more advanced techniques like:
- Hidden Singles (looking at units rather than individual cells)
- Naked Pairs and Naked Triples
- Pointing Pairs and Box/Line Reduction
- X-Wing, Swordfish, and other fish patterns
- Colouring techniques
- Advanced logical chains
However, these advanced techniques often work by eliminating candidates until they create Naked Singles, which you can then fill in to progress further. In this way, Naked Singles remain the ultimate goal of all Sudoku techniques.
Practice Strategy
Building Your Skills:
- Start with easy puzzles that are solvable using only Naked Singles
- Scan systematically – check cells row by row, or focus on nearly-complete units
- Look for constrained areas – cells surrounded by many numbers are more likely to be Naked Singles
- Update candidates immediately – when you place a number, update all affected cells
- Develop speed gradually – accuracy is more important than speed when learning
- Check your work – if you get stuck, verify your previous placements
Conclusion
The Naked Single is the heart and soul of Sudoku. It embodies the pure logic that makes the puzzle so satisfying: when only one option remains, that option must be correct. There's no guessing, no uncertainty – just clear, undeniable logic.
Mastering Naked Singles means developing the ability to quickly analyse a cell's three constraining units (row, column, box) and identify when those constraints leave only one possibility. This skill becomes second nature with practice and forms the foundation for understanding all other Sudoku techniques.
Every journey through a Sudoku puzzle, no matter how complex, is really just a series of Naked Singles waiting to be discovered. Some are immediately visible, whilst others only emerge after applying sophisticated techniques. But in the end, they're all Naked Singles – the fundamental building blocks that transform an empty grid into a completed masterpiece.