Naked Single




The Naked Single technique is (beside the Hidden Single technique) one of the first things you will come up with when solving your first Sudokus.

A Naked Single is a single (a solution) that results from all other cells in it's regions (row, column, box) being already taken by other numbers.

Here is the easiest example.

All cells in that row already have a single number in them, so the only empty cell in that row must be the last missing number, in this case it is the 9.

This, of course, also applies to other regions, namely rows and boxes, in the same way:

So far, it looks exactly like a Last Digit. So where is the difference? The difference here is that we don't just necessarily look at one region. We will see what this means in the following paragraph.

Easier than Hidden Singles?!

You now might think to yourself: "Wow, those are really easy to spot", and you might be right about this example, but there are many Naked Singles that are quite tough to spot.

This example is a bit harder, wouldn't you agree?

(Here, the cell in the middle sees all numbers except a 6. So it must be a 6.)

... and yet a bit harder...

(It is still the same 6 that is the Naked Single. Only the 4 changed its position, so it is not seen via row, but via box.)

And finally, how it might look in a real game. Still easy to spot?

When and how to look for Naked Singles

Oftentimes it is easier to spot Hidden Singles than Naked Singles, so I generally look for Naked Singles after I've looked for Hidden Singles, unless the Hidden Singles are very obvious.

As with Hidden Singles, it is more efficient, to start looking for Naked Singles in those cells that see many other fixed numbers.

For example these cells.

Take the 6 from before for example.

This cells sees nine other cells with fixed numbers in them. Two of these numbers are the same, but there are still eight distinct numbers that this cell sees. The ninth number must therefore be in that one cell.

After finding the 6 we should now first think of how this 6 affects our grid.

We find that there is another cell which is interesting (because it sees many fixed numbers).

That one sees eleven numbers. Some are doubled, yet still there are eight distinct ones. The missing number is, again, the Naked Single (7).

If we are keen on finding more Naked Singles, we continue like this.

Off by one or two

Oftentimes your search for a Naked Single will be off by one or two numbers, like with this cell.

Here, our cell sees nine other cells, but unfortunately two numbers (5 and 6) are occurring twice, so the cell only sees seven distinct numbers.

Seven is one too few, so we know that we have reduced the possible candidates to two numbers: 3 and 7.

We could now be sad and look at another cell, or we could notate our findings, so that we do not forget that we have almost found out this cell's solution.

For this cell, there can only be two numbers: 3 and 7. Those are the cell candidates.

In Standard Notation the cell candidates are put in their respective place within the cell.

In Cell&Box Notation we will place the cell candidates in the center of the cell.

Either way, we now do not need to remember that there are only two candidates left for that cell.

As soon as we, e.g. find out, that there is a 3 in the bottom left, we (as always) check how that newly found 3 influences our grid. We follow along the row and see that there is a cell with only two candidates, one of which is a 3.

We can eliminate that candidate, and the only candidate remaining is the 7, which is therefore that cell's solution.

When viewed from cell candidates' perspective

The connection of Naked Singles to cell candidates is very straight forward.

Every time there is only one cell candidate left for a cell, that is a Naked Single.

They can be easily spotted, once you notate cell candidates (and keep them updated).

Here are two examples: