One possible digit, or one possible position?
A naked single answers a question about one cell: which digits can go here? A hidden single answers a question about one digit in a whole unit: where can this digit go? Both produce a certain placement. What changes is the evidence you inspect.
Learning the difference helps you find more moves on an Easy board and avoids a common mistake with notes. A lone written mark may represent a complete list of one possibility, or an incomplete list with several missing possibilities. The puzzle supplies a naked single only in the first case.
Our diagrams use original, verified positions and complete logical candidate lists. Rows and columns are counted from the top left. A unit means one row, one column or one outlined 3×3 box. The term “single” does not mean that the unit has only one blank.
The naked single: intersect three restrictions
Take r1c5 in the first diagram. Its row rules out 6, 9, 8, 2 and 7. Column 5 also rules out 3, while the top middle box rules out 1 and 4. All digits except 5 are excluded by an existing number in one of those three regions. Therefore r1c5 must be 5.
Board overview
View the whole grid first. Zoom in to read candidates and their coordinates.
You can prove this naked single without listing every possible position of 5 elsewhere in row 1. The decisive fact is local to the cell, although the exclusions come from three overlapping regions. When you have verified that 5 is its complete list, enter 5 and clear its small note.
The after view shows the same position with that placement applied. Other cells in its row, column and box lose candidate 5. A placement can therefore create another naked single even when no new printed clue has appeared.
Board overview
View the whole grid first. Zoom in to read candidates and their coordinates.
The hidden single: inventory a whole unit
Now examine row 2 in the next position. r2c5 has candidates 3 and 6. You cannot solve it by the cell question alone. However, row 2 needs a 3, and its complete candidate inventory gives 3 exactly one position: r2c5.
Board overview
View the whole grid first. Zoom in to read candidates and their coordinates.
Suppose r2c5 were 6. Then row 2 would have no cell left for 3. That violates the requirement that the row contain all nine digits. So r2c5 is 3, and its candidate 6 disappears as a consequence of the placement.
Board overview
View the whole grid first. Zoom in to read candidates and their coordinates.
A hidden single can occur in a row, column or box. You need to examine one whole unit’s positions for a digit; you do not need that digit to have only one position in all three intersecting units. One valid unit argument is sufficient.
Compare the evidence side by side
| Question | Naked single | Hidden single |
|---|---|---|
| What do you inventory? | All legal digits for one cell | All possible positions of one digit in a unit |
| What is reduced to one? | The cell’s candidate list | The digit’s position list |
| Can the target cell have other candidates? | No | Yes |
| What must be complete? | The target cell’s list | Every position of the chosen digit in the chosen unit |
| What follows? | Place the only candidate | Place the digit in its only position |
Either form may be visible without writing every candidate. For a naked single, the filled digits around a cell may exclude eight possibilities directly. For a hidden single, scanning the existing copies of a digit across a box may leave one square. Pencil marks make the proof easier to inspect; they do not create the proof.
False naked single: a possibility you did not write
If a cell permits 2 and 7 but your notes show only 2, entering 2 from the written list is unsupported. Check its row, column and box: which placed number or established deduction actually excludes 7? If you cannot name one, keep 7 as a possibility.
The counterexample below deliberately changes the position behind the first example. Several restricting entries have been removed, and the complete candidates have been rebuilt. The highlight identifies the changed cells. r1c5 no longer has a one-digit list; the old proof cannot be transferred to the new board.
Board overview
View the whole grid first. Zoom in to read candidates and their coordinates.
Dashed borders mark changed givens; inspect the purple cells to see why the original rule no longer applies.
This is also why erasing a mistaken full-sized entry can require more than removing that number. Its neighbors may regain candidates that the old entry wrongly ruled out. The notes guide gives a practical update routine.
False single 2: a position you did not check
A hidden single is also vulnerable to incomplete notes. Seeing a 3 mark only at r2c5 does not prove that the row’s other blanks reject 3. Rebuild the positions of 3 across the whole row before using the argument.
In the changed version of our hidden-single example, removing a restricting entry lets 3 occur at both r2c1 and r2c5. The row must still contain a 3, but it no longer tells you which of those cells contains it.
Board overview
View the whole grid first. Zoom in to read candidates and their coordinates.
Dashed borders mark changed givens; inspect the purple cells to see why the original rule no longer applies.
Exercise 1: prove a naked single
Find the complete candidate list of r2c5 in the Easy position. Select its certain digit, then identify the kind of single. You should be able to justify the move even if someone covers the other cells’ pencil marks.
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Answer: r2c5 = 7, a naked single. The cell’s full candidate set contains only 7. You are proving that eight digits cannot occupy that cell, rather than proving that 7 has only one position in an entire unit.
Exercise 2: answer the position question
Inspect every empty cell in column 4 of the next position. Which digit can fit in only one of them? Notice that the target cell itself still shows two candidates.
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Answer: r1c4 = 2, a hidden single in column 4. r1c4 has candidates 2 and 5, so it is not a naked single. Column 4’s need for a 2 forces the placement and removes the alternative 5.
Use both scans in a solving loop
After each confirmed placement, look first for one-candidate cells among its neighbors. Then scan the affected row, column and box for a hidden single. These are small, repeatable tasks that exploit the information you just added.
When neither scan advances the board, do not assume you have missed a single forever. Medium puzzles can require candidate eliminations such as locked candidates or pairs before a new single appears. The stuck-puzzle guide shows how to make that transition. A staged Hint can also highlight the relevant area and explain a step against your current entries, without requiring you to follow the published solution order.