Naked Singles
A cell with only one possible candidate — the simplest and fastest placement in Sudoku.
What is Naked Singles?
A Naked Single (also called a Lone Single, Forced Cell, or Singleton) is a cell where only one digit can legally be placed. All other digits 1–9 are already present in the same row, column, or 3×3 box, leaving exactly one possibility. When you look at the cell's candidates and strip away every digit that appears anywhere in its row, column, or box, only a single digit survives. Naked Singles are often the very first technique beginners learn because the logic is immediately visual and intuitive — if 8 out of 9 possible digits are eliminated, the remaining digit is the answer. This technique is foundational: it delivers fast, confident placements with no risk of error. While Naked Singles alone aren't sufficient to solve most puzzles beyond the Easy level, they are always the first technique to check, and they frequently appear as cascading discoveries after more complex eliminations. An important solver discipline is to always resolve all Naked Singles on the board before applying any other technique — this ensures you're working from the most up-to-date candidate information.
When to Use Naked Singles
Use this as your very first technique, before anything else. After placing any digit (whether by Naked Single or any other method), immediately rescan the affected row, column, and box for newly created Naked Singles. Naked Singles most commonly appear in the middle and late stages of a puzzle as more digits fill in and cells become increasingly constrained. However, in heavily-pre-filled puzzles (like beginner-level grids with 35+ given digits), Naked Singles may appear right from the start. Always resolve every Naked Single you can find before escalating to more advanced techniques — they are free points that cost no mental effort and generate further information for your next moves.
How to Apply Naked Singles — Step by Step
- 1
Scan empty cells systematically
Move through each empty cell on the board in a consistent order (e.g., left to right, top to bottom). For each cell, look at all other cells in its row, column, and 3×3 box and collect the digits that are already placed. You are building the exclusion set for that cell.
- 2
Count remaining candidates
Subtract the collected digits from the complete set {1, 2, 3, 4, 5, 6, 7, 8, 9}. The digits that remain are the valid candidates for that cell. If exactly one digit remains — you have a Naked Single. There is only one digit that can possibly go in this cell given the current state of the board.
- 3
Place the digit immediately
Write that digit into the cell with confidence. No further logic is required — this placement is 100% certain as long as your candidate elimination was correct. Mark it clearly so you don't re-scan it.
- 4
Update all crossing units
After placing the digit, remove it as a candidate from all other empty cells that share the same row, the same column, or the same 3×3 box. This often creates new Naked Singles in those cells — so immediately re-scan all affected units before moving to the next empty cell. This cascading update is critical to efficient solving.
💡 Pro Tip
After placing any digit anywhere on the board — regardless of which technique you used — always re-scan the board for new Naked Singles before applying more complex techniques. A single placement often creates a cascade of 3–5 new Naked Singles in a chain reaction. Experienced solvers develop a reflex to immediately check the "neighbors" (same row, column, box) after every move. If you use pencil marks (candidate notation), Naked Singles are instantly visible as any cell with only one number written in it.
Practice Naked Singles Now
Put this technique to the test on a live puzzle. The Practice Mode lets you work through real examples with candidate marking.