# Counting 1-9

# Also known as Naked Single

This technique is known as 'Counting' because you need to 'count' through all the possible values for a cell, with the hope of finding that only one possible value can be placed there.

7 | ||||||||

5 | Y | 3 | ||||||

1 | 4 | |||||||

9 | ||||||||

8 | ||||||||

2 | ||||||||

So, in the example grid above, if we count for the cell highlighted in green and marked Y, we see that:

- 1 is taken on the subgrid;
- 2 is taken on the column;
- 3 is taken on the row;
- 4 is taken on the subgrid;
- 5 is taken on the row;
*6 might*be possible on this cell, so we need to remember that;- 7 is taken on the column;
- 8 is also taken on the column;
- And finally, 9 is taken on the subgrid.

So, by the time we have counted through all the digits, *in this instance *we have found that there is only one cell value possible, that being 6.

**Hint: **Sometimes, it is easier to look at a particular row, column or subgrid, and make a mental note of what numbers are still needed in that region - though most people will only find this convenient if there are just 2-4 cells remaining to be filled in that region. For example:

9 | ||||||||

4 | 1 | 6 | ||||||

7 | 2 | 3 | ||||||

Y | 5 | 8 | ||||||

9 | ||||||||

4 |

So, looking at the central subgrid, we see that values 4, 7, 8 and 9 are still needed in this subgrid. We can then look at each of the four empty cells in the subgrid, looking along the rows and columns and comparing to our little list of 4, 7, 8, 9.

We soon see that the highlighted cell marked with a green Y has 4, 8 and 9 in its row and / or column, so the value that goes there must be 7. Overall, this technique can prove a lot easier than trying to count through the numbers 1-9 for each and every cell!

#### Why 'Naked Single'?

This technique is known as Naked Single by some because, if you were to write in all the possible values for a cell, the list would come to just one number! So, if you were able to do that for all cells, it would be very obvious which cell(s) had only one possible value in - they stand out! Compare this to the cross-hatch method where (in the example we provide) if we were to look at the list of possible values on the cell that we eventually decided would be value 8, we certainly would not be able to say that 8 was the *only *possible value for that cell.

If you are unsure of any of the terminology we use, you may find it helpful to refer to our Glossary.

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