Naked Singles and Hidden Singles Explained

These two patterns finish most Sudoku puzzles between them. They are worth naming because you find them by asking two different questions, and knowing which question you just asked tells you where to look next.

Both examples below use the same row as the pencil marks guide, marked the same way.

A naked single

A naked single is a cell with one candidate left.

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One cell, one candidate. That is a naked single.

The picked-out cell reads 3 and nothing else. Its row, its column and its box between them use the other eight digits, so 3 is the only thing that fits and it goes in.

You do not strictly need pencil marks for this. The centre cell of this same puzzle is a naked single too, and the step-by-step guide finds it by reading its row and column out loud. What the marks change is that you stop having to look: once a unit is marked, its naked singles are already sitting there in the notation.

A hidden single

Now read the same row the other way round. Instead of asking what this cell can hold, ask where this digit can go.

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Read down the lists instead of across them: 8 appears once.

The five marked cells read 23, 278, 237, 36, 3. An 8 appears in exactly one of those lists. The row has to contain an 8 somewhere, and only one cell will still accept one, so that cell is the 8.

Look at what that cell says on its own, though: 278. Three candidates. Read by itself it tells you nothing, and it is not a naked single by any reading. The cell has not run out of options — the digit has. That is where the name comes from. The answer was in the notation, but not in the direction you were reading it.

The same row hides a second one. A 6 also appears in only one list, so that cell is a 6, even though it reads 36 and looks undecided.

The same thing without pencil marks

Cross-hatching, from step 2 of the step-by-step guide, finds hidden singles with nothing written down at all. Here is that same 8, found in the box instead of the row.

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The same answer, found without writing anything down.

The bottom-left box needs an 8 somewhere among its nine cells. Four 8s already on the board decide where:

The 8 in the seventh row rules out that row of the box.
The 8 in the ninth row rules out that one.
Two of the box’s three remaining cells then go: the 8 in the first column takes the left one, the 8 in the third column takes the right one.

One cell survives, and it is the cell the marks pointed at.

Two routes, one answer. Which one you use depends on what is already on your page. If the unit is marked, read the marks. If it is not, cross-hatch — doing one digit across nine boxes is much less work than marking eighty-one cells to learn the same thing.

Which to hunt first

Naked singles, because they are cheaper to spot and because they breed. Every digit you place removes a candidate from up to twenty other cells, and some of those cells were one candidate away from being finished themselves. Clearing them out first means the board does part of your next scan for you.

Hidden singles are the fallback when the naked ones dry up. Work one digit at a time and sweep the boxes first, then the rows and columns; boxes pay out fastest because they are compact and a single clue outside one can eliminate three cells inside it.

A puzzle rated easy or medium is usually nothing but these two, alternating, until the grid is full. When both are exhausted and the grid is not, you have reached the point where a puzzle earns its difficulty rating, and the techniques past here read several cells at once instead of one.

Four ways this goes wrong

Calling a two-candidate cell a single. 36 is two digits. A cell is a naked single at one candidate and at no other number.

Checking only the boxes. Boxes are the most productive place to cross-hatch, which is why most people stop there. A digit can be just as hidden in a row or a column, and those are the ones still sitting on the board when you decide the puzzle is stuck.

Not updating the marks after placing a single. The placement you just made usually creates the next one, and it only shows up if you cross the digit out of its row, column and box first.

Hunting the hidden ones first. It works, and it is slower. Sweep for naked singles, place everything that falls out, and only then start asking where each digit can live.

Where to go next

Pencil marks covers the notation both of these read from, and how to play Sudoku puts the two patterns back into a working order. Everything published so far is on the Learn index.