A Lone Single is when a cell has only one pencil mark left. They are the result of all your hard work – filling in & erasing pencil marks. When you get a cell down to one candidate, you have solved that cell!
The popular computer program Sudoklue calls Lone Singles “Naked Singles”.
All you need to do is pull out your eraser, erase that single pencil mark, and fill in the cell with your pen, right?
Well, yes – but there is another important step you must take. In most cases, filling in a cell will eliminate candidates in other pencil marked cells. So be very careful to look at all the other pencil marked cells in your cell’s row, column, and block - and erase any corresponding pencil marks.
For example, in the sample below, you can see that the green cell must be a “3”. Excellent! Get your pen and fill it in. But also notice the other cells that are affected. Suddenly, this new “3” makes all of the pink pencil impossible as candidates! You'll want to erase them.
You may notice that in erasing these pencil marks, you are creating at least one other lone single. Excellent! Move to that cell, rinse, and repeat...
Very often, when a puzzle gets down to the last 10 or so unsolved cells, a “chain reaction” of lone singles occurs, and the puzzle can be completed in seconds.