Naked Single - The Most Fundamental Solving Technique in Sudoku
A Naked Single occurs when only one candidate remains for a given cell. It is the first technique every Sudoku solver should master, and Easy-level puzzles can be completed using this technique alone. This article explains how to spot them efficiently and apply them effectively.
What Is a Naked Single?
A Naked Single refers to a situation where only one possible digit remains for a specific cell. After eliminating all digits already placed in the cell's row, column, and block, if only one candidate is left, that digit is confirmed. For example, if a cell's row already contains 1, 2, 3, 5, 7, 8, 9, the candidates are narrowed to 4 and 6 from the row constraint alone. If the column also contains 4, then 6 is confirmed for that cell.
How to Find Them Efficiently
The most reliable way to find Naked Singles is to use pencil marks and write out all candidates for every cell, but this is time-consuming. A more practical approach is to focus on intersections where heavily populated rows, columns, and blocks overlap. The more constraints that converge on a single point, the more likely candidates are to be narrowed down. In particular, intersections where a row has 6-7 digits and a column has 5-6 digits are hotspots where Naked Singles frequently occur.
Characteristics of Puzzles Solvable by Naked Singles Alone
Easy-level puzzles are designed so that a chain of Naked Singles alone can complete the entire grid. Confirming one Naked Single creates a new constraint that triggers another Naked Single elsewhere. This chain reaction propagates across the puzzle until every cell is filled. In puzzles with 36 or more clues, this chain continues unbroken, making advanced techniques unnecessary.
The Limitations of Naked Singles
At Medium difficulty and above, you will inevitably reach a point where Naked Singles alone cannot make progress. Every cell has 2 or more candidates remaining, with no cell that can be confirmed. Breaking through this wall requires the next level of techniques, such as Hidden Singles and Naked Pairs. While Naked Singles use the approach of finding a cell with only one candidate, Hidden Singles take the reverse approach of finding a block where a specific digit can only go in one place.
Naked Single vs. Hidden Single
The naked single and the hidden single are both basic techniques for fixing a single cell, but the direction you look is exactly opposite. The naked single is a cell-centric view: you pare down a cell's candidates by the row, column, and block constraints, and when one remains, it is fixed. The hidden single is a number-centric view: when there is only one place in a unit where that number can go, it is fixed. The big difference is that a naked single cell has only one candidate, while a hidden single cell is fixed while still holding other candidates. Once you can consciously switch between the two, stalls decrease greatly.
Where on the Board to Search
To find naked singles efficiently, the iron rule is to focus on areas already filled with many numbers. A cell's candidates narrow the more numbers are placed in the row, column, and block it belongs to. Therefore, an intersection where all three units are well filled - a place where constraints concentrate - is a hotspot where naked singles tend to arise. Conversely, no matter how long you stare at an area with many empty cells, candidates will not narrow and you only waste time. The habit of scanning preferentially from densely filled places, rather than gazing idly at the whole board, directly leads to speed of discovery.
The Chain That Placement Brings
The value of a naked single lies less in filling a cell than in the chain it triggers. When you fix a number in a cell, that number is erased from the candidates of the same row, column, and block. Then another cell's candidates often drop to one, producing a new naked single. Easy puzzles are designed to be solved to the end by this chain alone. If you make a habit of immediately reviewing the surrounding affected cells each time you fix a number, you can advance through the chain without dropping any. Conversely, neglecting the review after a placement makes you miss a naked single that was just born.
Its Place in Practice
The naked single is the most basic technique, the first you use in any puzzle. No matter how hard the problem, the standard approach is to first clear what you can fill with naked singles and hidden singles in the opening, and proceed from there to advanced techniques. If you neglect the basics and only hunt for hard techniques, you overlook the easy placements at your feet and take a detour. Conversely, the more quickly and accurately you handle the basics, the more time and capacity you have to concentrate on the hard spots. Plain as it is, the precision of the naked single is what supports the foundation of the whole solution.