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Sudoku Solving Techniques: Single Candidate
Single candidate works by looking at a particular square and working out which numbers would be valid candidates for that cell. If that cell only has one valid candidate, then we can conclude that the value of that cell must be that single valid candidate
Here are a couple of examples.
Look at the cell hilighted in green, and work out which numbers could fit in that cell within the rules of Sudoku.
This cell happens to be in a row which is already fairly full. We can eliminate all the numbers that are already in this row, i.e. We can eliminate the numbers 2, 3, 4, 6, 7, and 8, this only leaves us with the numbers 1, 5, and 9 as valid candidates.
If we look at what is already in the same column, we see that there is a 5 and a 9 already in the same column, so we can eliminate the numbers 5 and 9. This leaves us with just the single valid candidate, and that is 1.
This example is little more complicated as you have to look at the 3*3 squares as well. Look first at the numbers already taken in that column, we can eliminate the numbers 3, 4, 5, 7, and 9. This leaves us with 1, 2, 6, and 8.
Next, look at the numbers already in that row. We already have the numbers 2, 3, and 4 in that row, so we can also eliminate these. It doesn't matter that we've already eliminated the number 2, this will happen more and more as the grid fills. This leaves with the numbers 1, 6, and 8.
Now, look at the numbers in that 3*3 square, we already have the numbers 3, 6, 7, and 8 in that 3*3 square, so we can eliminate those from our valid candidates. This just leaves us with one single valid candidate: 1.