Advantages of distillation into parallel binary grids

Advanced methods and approaches for solving Sudoku puzzles

Advantages of distillation into parallel binary grids

Postby zebedeezbd » Mon Sep 19, 2005 11:24 pm

I have recently been experimenting with an alternative method of notation that can facilitate certain aspects sudoku solving. There are several pros and cons that I would like to mention for discussion.

It involves distilling the puzzle into nine separate binary puzzles, so that the state of play for each number can be seen with clarity. Each grid deals with a particular digit and is concerned simply with whether each cell is or is not that number. The grids are binary in the sense that each cell is marked with a true/false value showing whether or not that digit is in that cell (or blank for "don't know yet"). I use a cross to mark false and a large dot for true.

The first negative aspect is that to do this entirely by hand is an awful lot of effort to prepare the nine grids and mark off all the initial possibilities. However, it is a mindless job easily carried out by a spreadsheet. Below is The Sunday Times Su Doku 6 distilled into its nine constituent binary puzzles:


The dots and crosses that have been added so far are by the application of basic sudoku assumptions alone, namely no repeats in a block, row, or column, coupled with the fact that a cell obviously cannot be a given digit if it is already known to be another digit.

Hidden Singles are very obvious using this notation. There is a glaringly obvious one in the centre block of grid 6, another in row 1 of grid 2, and yet another in grid 4.

X-Wing configurations are also very easily spotted. There is one in grid 6 (rows 1 and 3, columns 2 and 4).

Swordfish and Turbot configurations are relatively simple to find with the puzzle laid out like this as well.

Another technique that is particularly easy to implement with this notation is the elimination of candidates when a given digit can only occur in a particular row or column of a given block.

With a little effort some naked pairs can be located, but because these require cross-referencing between the grids they cannot be spotted with great ease. Naked triples are tougher to find, generally.

That is one of the interesting things I have found about this approach to solving sudokus. Some of the techniques considered to be higher-level (such as X-Wing and Swordfish) are actually much easier to implement than lower-level techniques (like naked pairs) that are more easily found using conventional notation.

This makes it of limited use as a solution method alone. (I eventually got stuck on the above sudoku on a very hard-to-spot triple.) But when solving tough puzzles, it would be an interesting approach to use this method in parallel with a conventional grid of candidates.

Does anyone use anything along these lines already?
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Postby Myth Jellies » Tue Sep 20, 2005 5:54 am

My Pattern Overlay Method (seems it's been shortened to POM) makes use of these kind of plots. POM explanation thread
Myth Jellies
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Postby Anette » Tue Sep 20, 2005 8:39 pm

zebedeezbd, I do almost the same as you. I have an Excel sheet where I do this, but have also created a 81*81 grid that displays all remaining candidates for each square.

I agree that it makes especially spotting X-wings much easier. I also tried to put in counters that look for rows, columns and boxes with only 2 or 3 remaining candidate squares for a certain number (to help me spot hidden pairs and triplets), but haven't foud that so useful.

It could probably be done much better if I knew visual basic, but it is good enough to help with the tedious elimination of candidates.
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Postby Anette » Tue Sep 20, 2005 8:40 pm

27 * 27 grid, not 81 * 81
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Postby PhatFingers » Thu Sep 22, 2005 6:22 am

Simple Sudoko does this with "Filters". Click on the number buttons 1-9 and it paints all remaining candidates of that number.
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Postby cheesemeister » Sun Oct 02, 2005 4:12 pm

Thanky muchly, I was having a bit of trouble working out what x wings (and obviously all the various spin off techniques) were for let alone how to find them, and your binary distilation has made what they're for crystal clear, now I just have to figure out how to find them before I even think about swordfish or anything more complicated.
Any chance of posting a link to where the excel bits can be downloaded from?
P.S. what's a Turbot? I've never even seen the term before...
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