As I've already done on the Sudoku UK and on the Sudoku Programmers Forums, I'd like to announce here the publication of my new book, "The Hidden Logic of Sudoku".
Detailed information (including full introduction, full conclusion and an extended excerpt) can be obtained from my web pages (http:www.carva.org/denis.berthier).
Complements can also be obtained from the discussions we've already had in the two forums mentioned above.
The approach taken is the book is player oriented from the start; all the resolution rules rely on the same three universal representations that can be used to solve any puzzle.
Starting from the systematic logical analysis of all the natural symmetries of the game, I've devised an extended Sudoku Board (freely downloable online), a new global conceptual framework and a new resolution method based on this extended board. All the resolution rules used in the book are proved once and for all (contrary to many advanced techniques that need a specific reasoning for each case you meet). The resolution job is thus centered on the spotting of the patterns underlying the rules.
The extended board is composed of the standard board (the row-column or rc representation) plus two auxiliary boards, the row-number (or rn) and the column-number (or cn) representations.
Using the auxiliary boards, complex patterns become obvious. For instance:
- in the appropriate board, a Hidden Quad looks like a Naked Quad;
- in the appropriate board, a Jellyfish also looks like a Naked Quad;
- conjugacy links look like bivalue cells;
- some complex (but not all) AILs look like simple xy-chains;
Apart from the usual elementary and medium level resolution rules (for subsets and interactions), I've introduced:
- xyt-chains, a powerful extension of xy-chains, but still chains (i.e. linearly ordered sequences of linked cells) and not nets (defined with only a partial order on the cells);
- hidden chains; they are the counterparts of usual chains, but in the auxiliary rn- and cn- spaces; in these spaces, they look like ordinary chains do in rc-space; hidden chains are a very powerful tool.
Although the set of rules thus defined is very restricted, it is enough to solve 99.7% of the famous Gordon Royle collection (of 17-minimal puzzles) and 97% of the puzzles generated by the suexco pseudo-random generator.
Since it does not solve all the puzzles, this approach does not reduce to nought all the work that has been done by others for inventing subtle resolution techniques. But it may significantly decrease the complexity of many puzzles, as I have shown for Ruud's top1000 list. It may therefore allow medium level players solve puzzles that would otherwise be considered as very complex.