Hello to all,

I am starting this thread to share some ideas on Sudoku logic and perhaps get feedback from the experience in this forum. Although I'm a computational junkie, my experience with the Sudoku world is limited. Everything is presented on my (non-commercial) website dedicated to the purpose along with numerous examples and many 3D images:

http://sudokuone.com

The approach is like a local area set theory. It focuses on global and regional properties of sets rather than candidates and implications. It does this using cover sets from set theory and a logical rank that defines regions. Regions and boundaries are then related to multiple linked logic. This, combined with 3D symmetry, produces a few simple rules that are not restricted by geometry, set type, or number of candidates. Unlike this quick description, the rules themselves are simple and easy to apply. I have been using them for over a year and I cannot find anything they do not account for, not to mention what they can explain or predict.

Some concepts are not new. Cover sets are used with fish and in fact, are fish. Cover sets are also the basis for the Subset Constraint Theory that I have seen here and in part the two approaches are the same. Cover sets in turn can be derived from other principles including permutations. Sudoku's 3D symmetry is also well known but not widely used. This approach is developed in 3D from the start without reliance on single-digit logic or bi-value sets.

I hope some of this is useful or at least interesting. I'm also interested to hear how it might be refined, made more useful. Thanks.

Allan Barker

[8-6-08]

Uploaded major revision of SudokuOne Web Site. Main differences are:

. Much shorter, the entire set theory derivation and explanation is now on one page.

. A new section with many simple examples of set theory principles.

. Full attention to previously sketchy areas, i.e., triplets, rank zones, summing of rank effects.

As usual, all feedback is welcome. rab.