Sudoku solving method

Kind of pointless for the usual 9x9 ones, but when you get 25x25 monster sudokus it can be quite efficient.

This idea uses gimp and saves images in xcf format.

The idea is to make information visible and to try to gain an overview of the situation as well as to focus of special aspects of it. To achieve this I use layers in gimp which I show and hide to see different things.

(If the text so far does not make sense to you, skip the rest of the page and do something useful instead.)

These are my example files:

• 1_template.xcf
• 2_ink.xcf
• 3_initial_conclusions.xcf
• 4_start.xcf
• 5_stuck.xcf
• 6_done.xcf
• a_little_helper.gif
• another_helper.xcf

1-5 are explained below. The "little helpers" are just some stuff I found useful and thought you might too.

1. template

   Copy this file to your hard drive.

   Open the file in gimp (I don't know if this works in any other program). Zoom in to as big as your monitor can handle. (The idea is to manipulate pixels.)

   The template file consists of a number of layers. From back to front:

   • Background is a plain sudoku layout (without numbers). The yellow and white pattern should be interpreted as just "two shades of white". I did that because it looks pretty, and it also makes it easier to tell the difference between different pixels in the 25x25 case.
   • Ink is where you will copy the information from the magazine.
   • Starting position is where you put conclusions based only on "ink" (I could have made this the same as "ink" but I thought it looked tidier this way).
   • pencil This is where your solution goes.
   • 1-9 are layers that focus on each of the numbers. They are kept invisible and looked at one at a time. Their purpose is to "filter out" uninteresting information. To begin with they contain a pattern in "transparent black". The idea with this is to make the interesting pixels stand out but without completely hiding the other pixels.
2. ink

   Here I have filled in the "ink" layer with an example. Instead of numbers I have coloured groups of nine pixels with red and blue. You could say that red means "yes" and blue means "no" and the pixels are grouped like the numbers 1-9 on a telephone. I only paint a pixel blue or red if I am sure. Otherwise it will show up as white or yellow.

3. initial conclusions

   To begin with there are a number of conclusions one can make. A red pixel means that 20 other pixels cannot be red, so they have to be blue. In this file I have filled in those first conclusions in the "starting position" layer. Now everything that is not possible shows up as blue.

4. start

   Here I have filled in some information in the number layers. I have looked at the bright, non-shaded, pixels and if they are red the whole group has been painted over with red, if they are blue they have been painted over with blue. (gimp has a 3x3-brush which does this job a lot easier, also the "another helper" file contains some common patterns) (I hope that made sense.)

   Make a copy at this stage! It is a good starting position to get back to if you make an error during the solving.

   This is where the actual solving begins. Look at one number layer at a time and see if you can find groups of nine numbers where only one is unmarked. When you find one you move to the pencil layer and do the changes there (while keeping the number layer visible). Then go back to the number layer and fill in the information there too. (I already used the "I hope that made sense." comment, but here is one more: I hope that made sense. *sigh*)

   In the example 7 is quickly finished. Its layer is no longer interesting. Move it out of the way (or delete it).

   Continue until you get stuck.

5. stuck

   Hide the number layers and look at the solution so far.

   Think.

   Add more solutions by writing to the pencil layer.

   When you can't find anything more this way, go back to focusing on one number at a time. Continue alternating between these two methods until you are done.

6. done

   Smile! Be happy! Have a drink. Copy the numbers back to your magazine. (Or don't.)

A simpler version of this method is to write little dots with pencil on paper (these would be the same as the blue pixels in the example).