Hello all,

I try to follow up with all the new solving techniques that come up by frequently visiting this forum. However, since I’ve first started solving sudoku puzzles I was always thinking that there should be a SINGLE solving technique that solves ALL puzzles without going into trial & error, since there is only one rule. Well, the method that I present here (http://files.filefront.com/General+method+for+solvinupdf/;9583658;/fileinfo.html - with many examples), although I cannot prove that it solves all puzzles, it ‘encloses’ all the methods that I am aware of, meaning that each of the known techniques is an individual case of the method. Only the techniques which assume that only one solution exists (uniqueness tests) are not covered, since that information is not used.

In practice however, the method is not very significant, because it is easier to apply the individual techniques which narrow significantly the research field of a valid ‘pattern’ where eliminations can exist. Anyway, I am posting it in case other people had the same ‘obsession’ of this one method for all cases. And maybe use its framework to find other, new techniques, since only part of the ‘capabilities’ of the method are used in the current techniques –but this may be due to the geometry of the standard sudoku, in other variations with more complex geometry (X-sudoku, Windoku, ..., and especially Sukaku) I have found cases that cannot be applied to standard sudoku-.

The method works like X-Wing, where N rows are trying to cover N columns but ‘rows’ and ‘columns’ are more abstract objects. It is all covered by naive set theory and therefore sudoku obtains a strong link with maths and a simple but elegant math framework.

Also, when number N becomes large (it can go theoretically till half of all the 324 candidate sets) it is human impossible to apply the method, but it can be applied by a computer solver, which is what I am working on (some months now...), hoping that the program will give me new techniques for solving sudokus, if not for the standard grid, at least for its variations.

alex