Lesson:Naked Singles
Welcome to Intermediate! Let's master Naked Singles.
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💾 Saved locallyAbout This Lesson
Naked Singles is the formal name for what beginners often call "the obvious move" — a cell where only one digit is legally permitted. Every other digit from 1 to 9 has been eliminated by the row, column, and box constraints. The single remaining candidate is "naked" — fully visible and immediately placeable.
Naked Singles are the most fundamental technique in all of Sudoku. They require no pencil marks, no complex logic, and no candidate tracking — just a clear view of what digits already appear in the three units (row, column, box) that share the cell. Mastering Naked Singles quickly and accurately is the first step to solving puzzles of any difficulty.
On Easy puzzles, Naked Singles alone (combined with scanning) are often sufficient to reach a complete solution. On Intermediate and harder puzzles, Naked Singles appear repeatedly throughout the solve — each more complex technique ultimately creates Naked Singles that you then place.
How It Works — Step by Step
Step 1 — Look for near-complete rows, columns, and boxes
Cells that belong to units with 8 digits already placed have only one empty slot — that is a guaranteed Naked Single. Always check these first.
Step 2 — Enumerate constraints for a cell
For any suspicious cell, check the row (8 constraint digits), the column (8 more), and the box (8 more). The union of these three sets eliminates candidates. If all but one digit is eliminated, you have a Naked Single.
Step 3 — Place and propagate
Place the single candidate. Immediately check all cells in the same row, column, and box — some of them may now become Naked Singles too. Chain placements until no more Naked Singles remain.
When to Use This Technique
Always — after every placement, before anything else. Naked Singles are the fastest, most reliable step in Sudoku solving. Never skip to advanced techniques without first exhausting all Naked Singles.
Worked Examples
A cell in Row 2 sees digits 1, 3, 4, 6, 7, 8 in its row; 2, 5 in its column; and 9 in its box. The forbidden set is {1, 2, 3, 4, 5, 6, 7, 8, 9} — all nine! Wait, that means all are forbidden, which is impossible. Re-check. Row has 1,3,4,6,7,8 (six digits). Column has 2,5. Box has 9. Union: 1,2,3,4,5,6,7,8,9 — the cell must already be filled, or there is an error. Correct example: row has 1,2,3,5,6,7,8,9 (missing 4); column has 4 (so 4 is forbidden); no — wait, if 4 is in the column, it is forbidden. The cell needs the one digit not in its row. If only one is missing from the row and not blocked by column or box, that is the Naked Single.
Frequently Asked Questions
Are Naked Singles and single candidate cells the same thing?
Yes — "Naked Single," "single candidate cell," and "lone single" all refer to the same concept: an empty cell with exactly one legal candidate digit.
Can I always find Naked Singles without pencil marks?
On Easy puzzles, yes. On Medium and Hard puzzles, Naked Singles often exist but require full candidate tracking to spot efficiently, especially when the cell is not in a near-complete unit.
Related Lessons
Ready to test your knowledge? Try applying this technique in our Easy Sudoku challenges, Medium Sudoku puzzles or explore Naked Singles technique guide. Keep training to improve your solve times and master the grid!
Ready to Practice?
Apply this technique on a real puzzle from our daily or practice modes.