###### Counting

Once we get onto more advanced Sudoku solving techniques, we need to start keeping a count of the numbers which might possibly be allowed in each square. This is a little tedious to do, but quite straightforward, and well worth the trouble.

Let’s look at another sample puzzle, and see what values might possibly be allowed in one square, in this case [7,6], indicated here by the dark green square.

First we’ll look at the row this square lies in, and note the squares which are already filled in. We know that values can only occur once in a row, so therefore these values won’t be found in the square we’re examining.

Next we’ll look at the column this square lies in, and note the squares which are already filled in. Again, we know that values can only occur once in a column, so therefore these values won’t be found in our square.

The last bit of information we can gather comes from looking at the 3×3 box our square lies in. As in the other two cases, we know that any numbers already filled in in this 3×3 box will not be found in our target square.

Finally, we combine our 3 lists of numbers that *can’t* be found in our square to make one big list of ‘impossible’ numbers. Any number from 1 to 9 which can’t be found in this list is a possibility.

As you work out the possible numbers for each square, you’ll probably want to mark them on the puzzle. Something like this works quite well. As you deduce more information about the contents of a square, you can cross more numbers off.

Now that we’ve got counting sorted out, what can we do with it? We’ll see in Tutorial 3