Sudoku Assistant - The Sudoku Trainer and Solver

Pencil Marks

For when you can't get a cell value straight away

This techniques discussed previously are all about finding out what value a cell can contain directly... that is to say, if our search is successful, we get to fill in a cell value!

But what about all those times where we are not successful, and we find out that a certain number of values could be placed in a cell? A puzzle does not have to be very difficult before this type of thinking becomes necessary!

The solution to this is to write in the possible values in each cell - simple! As Sudoku puzzles are often printed rather small, some people find that writing the possible values into the cell is rather difficult or just about impossible. One alternative used by some is to mark dots in a grid - where the position indicates the value. The image below shows two possible methods for indicating '4, 7 and 9 could exist in this cell':

Showing two different types of pencil-mark commonly used in Sudoku

The grey digits in the second cell demonstrate the rough positioning that is used by some.

Which method you use seems to be a matter of taste - but both methods require that you 'cross out' some values at some time, when you find out that a cell can no longer contain a particular value.

Sudoku Assistant Approach

Sudoku Assistant uses the first technique to show pencil marks - and of course, you don't have to worry about crossing-out or erasing a mark you no longer need on a computer.

Cautions when using Pencil Marks

Although probably not an issue with computer software that can fill in pencil-marks for you, you might need to be cautious when using pencil marks. We suggest that you opt to follow some simple rules when writing them in:

  1. Do not use pencil marks too soon - unless you are very sure that you have found all the cells that can be solved using cross-hatching techniques;
  2. Early on, only mark pencil-marks as a result of using cross-hatching. In other words, you will be marking several cells in one subgrid with 'all the possible locations in this subgrid that 7 can go' - but don't do this if you will be marking more than 2 or 3 cells;
  3. If you are strict using this technique, then when you fill in a cell value you can do a quick scan of related rows, columns and subgrids for pencil-marks of the the same value. If you see any, you should cross them out... and if that leaves just one pencil mark of that value in the subgrid, then you have the location for your next cell placement.
  4. As soon as you start to write the results of counting into a cell you can no longer use the kind of shortcuts noted above - though harder puzzles will probably require you to do this at some stage during solving.

This issue is a parallel to the differences between the cross-hatch and counting searches - one shows you all the possible values that could exist in a particular cell, where the other tells you all the possible cells that you could place a particular value within a particular subgrid (or potentially row / column).

If you are unsure of any of the terminology we use, you may find it helpful to refer to our Glossary.

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