Naked singles: the first technique to master
When one cell has only one candidate left, the constraints have already written the answer.
What is a naked single?
For one empty cell, eliminate every digit already present in its row, column and box. If only one digit remains, that digit must go there.
How to spot one faster
Check cells surrounded by many clues and keep candidate notes tidy. A cell moving from three candidates to one becomes an immediate answer.
- Recheck the row after every placement
- Then inspect the column
- Finish with the 3×3 box
Why it matters
Many medium puzzles are chains of naked singles. Missing one can make the board feel frozen; finding it often unlocks several moves.
Worked example: combine all three regions
For an empty cell, suppose its row already contains {1, 2, 3, 5}, its column contains {2, 4, 6}, and its box contains {1, 7, 9}. Combine these sets: {1, 2, 3, 4, 5, 6, 7, 9}. The only digit absent is 8, so the cell must contain 8.
Do not count repeated exclusions twice. The 2 appears in both the row and column, but it is still only one excluded digit. If two candidates remain, you have not found a naked single.
Self-check and a common mistake
Exercise: a cell’s row, column and box together exclude {1, 2, 4, 5, 6, 7, 8, 9}. Which digit remains? Answer: 3. If 9 were not excluded, both 3 and 9 would remain and you could not fill it using this technique.
Incomplete notes can create a false single. Before committing a number, recompute the candidates from actual entries, not just your handwritten notes. After placing a digit, remove it from notes in the same row, column and box, then look for new singles.