Naked single: One cell, one candidate
Find cells with just one candidate and learn to check why the other eight digits are excluded, without guessing.
What you are looking for
A naked single occurs when an empty cell has only one possible candidate. You may also see it called a sole candidate. The deduction focuses on one cell and asks which digits can remain after checking its row, column and box. When eight digits have been excluded, the ninth must be the answer. The row need not be nearly full, because the exclusions can be spread across all three units. The word naked means that the single remaining possibility is visible in the complete, current candidate list for that cell.
A worked example using three units
Suppose you are examining r4c6. Its row already contains 1, 2, 4, 6 and 9. Its column rules out 3 and 5 as well. Its box rules out 8. Combining those exclusions removes 1, 2, 3, 4, 5, 6, 8 and 9. Only 7 remains, so r4c6 = 7. This is a local example: The lists describe the relevant constraints on that cell rather than a complete puzzle. The conclusion relies on the entries used for those exclusions being correct.
A repeatable way to check
Consider the digits from 1 to 9 in the same order each time. For each digit, check whether it is already placed in the cell’s row, column or box. A digit appearing in any one of those units is enough to exclude it. When using pencil marks, remove candidates that become impossible after a proven placement. One small mark is not a proof on its own if you entered your notes manually and missed another possibility. Recalculate the list when in doubt. Checking again is more useful than carrying an unnoticed mistake into later moves.
What changes after the placement
Once you place 7, no other cell in that row, column or box can contain 7. Remove that candidate from cells sharing a unit with r4c6, then inspect them again. A list such as {3, 7} might become {3}, producing another naked single. Do not remove 7 from a cell that shares none of the three units with the placement. Candidate updates have a precise reach. A chain of singles can solve many cells, but each link in the chain still needs a valid exclusion to support it.
Exercise and explained answer
For an empty cell, the row excludes 1, 3, 5 and 8; the column excludes 2, 4 and 6; and the box excludes 9. What can you enter? The answer is 7, because it is the only digit from 1 to 9 absent from the exclusions. Now change the exercise: The box no longer excludes 9, and there is no other reason to remove it. The remaining list is {7, 9}, so there is no single yet. Keep both candidates and look elsewhere. Recognising that you still need more information is part of solving logically.
If you have ruled out the other eight digits, what can you enter?
Cell r3c4 · Complete candidates: {7}
Now try it on the grid.
Return to an easy puzzle and look for a chance to use what you’ve learned.
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