A naked single is a cell that has one candidate left. A hidden single is a digit that has one cell left in a house. Both place a digit, and what separates them is which of the two you had to look at.
Why they get mixed up
Both techniques end the same way. One digit goes into one cell, nothing is eliminated directly, and no chain of reasoning is needed to defend the move. Both are called singles. On a bare grid you may never notice which one you used, because you simply see that a square has to be an 8.
The resemblance is strongest in one situation: a row, column or box with one gap left. A gap like that is both kinds at once. The house has used eight digits, so the cell has one left. The missing digit has one empty cell to go to, so the digit has one home. Both questions get the same answer, and someone who learns on these cells never has to find out that they are two different questions.
They come apart as soon as a house has more than one gap. The result is the same. What differs is what you looked at to be sure:
- A naked single is found by reading a cell. Its row, its column and its box leave it one candidate. With pencil marks the cell shows a single mark, and you can see it without looking at any other empty cell.
- A hidden single is found by reading a house. A digit has one cell left in a row, a column or a box. That cell may still show several candidates, so looking at it alone tells you nothing.
A house with one gap: both answers are yes
Column eight holds every digit except the 8, and its only empty cell is at the bottom. Ask that cell what it can be and the column alone leaves one digit. Ask where the 8 can go in column eight and there is one place. Both questions answer, on the same cell, with the same digit.
This is the case that makes the two look identical. It is the column doing the work, though. Along row nine and inside box nine the same 8 still has three cells open to it.
One mark in the cell, several homes for the digit
Now the bottom-right cell of box two. Its row holds a 1, a 3 and a 7. Its column holds a 1, a 4 and an 8, and its box holds five digits. Between them that is every digit except the 2, so the cell shows one pencil mark. It is a naked single.
Ask the digit and the answer changes. In box two a 2 could still go in four cells. Row three offers four, and column six offers four. No house has run out of room for the 2, so this is not a hidden single. The cell settles it and nothing else does.
Four marks in the cell, one home for the digit
The empty cell on the left of the same box's middle row shows four candidates: 2, 4, 7 and 8. Ask it what it is and it cannot say.
Ask the 8 instead. Row one already has an 8, and columns five and six each carry one lower down, so three of the box's four empty cells are closed to it. The fourth takes it, and column four gives the same answer from a different direction. That is a hidden single, and the pencil marks in the cell never pointed at it. The hidden single article shows how to hunt for these.
A cell scan finds naked singles and walks past hidden ones. A digit scan does the opposite. If you only ever do one of them, you will stall on grids whose remaining singles are all of the other kind, so when you run dry, switch.
The same split runs through the next chapter
Naked and hidden are not two names for singles only. They are the two directions you can read a house in, and the pair techniques split along exactly the same line.
A naked pair is two cells in one house that show the same two candidates and nothing else. You find it by reading cells. A hidden pair is two digits that have the same two cells left in a house. You find it by reading digits, and the two cells may be covered in other marks. Triples and quads follow the same pattern.
So the habit worth building here is not a list of techniques. It is the pair of questions. For any cell, ask what it can be. For any digit in any house, ask where it can go. The whole subsets chapter is those two questions, asked of two, three or four cells or digits at once.
The marked cell in row one can only be a 3. Is that a naked single, a hidden single, or both?
Ask the cell what it can be. Then ask where a 3 can go in row one.
Recap
- Look for
- A placement you are sure of. Then ask whether a cell told you or a house did.
- Scope
- Any cell and any house, with or without pencil marks.
- Result
- One digit is placed either way. The name records how you found it, not what it does.
- Tell-tale
- A single pencil mark means naked. A digit that appears once among a house's marks means hidden. A house with one gap is both.
- If it fails
- If a scan of cells finds nothing, scan digits house by house with the hidden single. If both come up empty, the grid needs an elimination first, and the naked pair is where that starts.