Puzzle Madness
Not logged in. [Register (free)][Login]

Sudoku Solving Techniques: Pencil marks

All easy and medium difficulty puzzles can be solved simply by using the single candidate and single position Sudoku solving techniques. To solve the harder Sudoku puzzles you will need to use pencil marks.
Look at each cell in the grid in turn, and write in small numbers all the candidates for that particular cell. If you were doing this on paper, you would use a pencil so that you could erase it later, hence the term 'pencil marks'.
Pencil marks themselves don't help you that much, but they do help you to use the more advanced Sudoku solving techniques
In this grid we have looked at each cell in the grid and written in small numbers all the candidates for that particular cell.
This process may seem quite laborious, and it is. In reality however you would only resort to pencil marks once you fail to make progress using the single candidate and single position techniques. Also, you would typically start writing pencil marks in the areas of the grid which you think are going to yield results first. So, if a section of the grid is mostly filled in and doesn't have many unfilled cells, that would be a good place to start with pencil marks.
This is how a single candidate would show itself in pencil marks. Here we have a cell with only one possible valid candidate. We can fill the green cell with a 7, and we can immediately conclude that the cell to the right must be a 9.
We didn't need to use pencil marks to find this, but it certainly made it easier to spot.
Look at the green hilighted cell, this is how the single position technique manifests itself using pencil marks.
If you look at all the other cells in that column you will notice that none of the other pencil marks include the number 8. We can conclude that our green cell must then be 8.