Candidate Lines

This is the first technique which doesn't actually tell you where to place a number, but instead helps you to determine places where you can't place a number! If you're using pencilmarks, then this will help you to remove candidates, and from there you should be able to make placements.

If you look within a box, and find that all of the places where you can put a particular number lie along a single line, then you can be sure that wherever you put the number in that box, it has to be on the line.

Even if you don't know exactly where to put the number yet, you can use this knowledge! You know that none of the other positions on that line (in the other two boxes) could contain that number, so you can remove those as candidates!


An explained example

Take a look at the bottom right box (box number 9):

Sudoku puzzle

There's only two places where the 4s can be - and they're in a line (a column).

Sudoku puzzle

What this means is that the 4s on that line must be in that box - and can't be anywhere else on the line.

Sudoku puzzle

Look for the other candidates for 4 in that column...

Sudoku puzzle

The result is that you can remove those two candidates for 4, leaving a 2 on its own - so straight away you can fill in another value!

Sudoku puzzle