The Hidden Logic of Sudoku
"A new conceptual framework for solving Sudoku puzzles with pure logic"
Second, revised and extended edition: November 2007
29.95 euros (paperback, 416 pages, Royal: 6.14" x 9.21" - 15.6 cm x 23.4 cm)
ISBN : 978-1-84799-214-7
Support print-on-demand publishing, buy this book directly from Lulu:
(First edition published by Lulu.com, May 2007, ISBN : 978-1-84753-472-9)
|© Denis Berthier. All the material in this page and the pages it gives access to are the property of the author and may not be re-published or re-posted without his prior written permission.|
| The Hidden Logic of Sudoku
provides the first systematic perspective of the logical
foundations and of the symmetries of the popular game. These
are fully exploited to define new kinds of resolution rules,
new graphical representations that may ease the solving
process and a precedence ordering of the rules consistent
with their logical complexity.
In addition to a few elementary rules, the very classical and basic pattern of xy-chains has been extended, as far as its underlying logic allowed, to a homogeneous set of chain rules of progressively increasing complexity. It suffices to solve almost any puzzle without making guesses, without dealing with chains of subsets or with nets and without assuming the uniqueness of a solution.
These rules are illustrated with a hundred puzzles, together with their full resolution paths. They have been tested in an Artificial Intelligence (AI) engine and tens of thousands of puzzles have been processed, leading to a precise evaluation of the efficiency of each rule.
This book is intended for Sudoku players of all levels: they will discover many new facets of the game and new types of resolution rules - introduced in a pedagogical way and set in a uniform conceptual framework based on patterns. It is also intended for teachers or students of Logic or AI: they will appreciate the strict logical foundations.
Keywords: Logic Games, Sudoku, Artificial Intelligence.
What's new in the second edition (pdf)
Press release (pdf)
Press release (french version) (pdf)
Extended Sudoku Board (pdf): This is a Sudoku Board specifically designed for the easy application of the Sudoku resolution method defined in the book. Using this board, complex hidden patterns will be made obvious. How it can be built and used is described in full detail in the book.
This board is copyrighted with the only goal that it will not be patented by anybody and will always remain available to the whole Sudoku community. Feel free to use it and to tell me about your experience with it.
Frequently Asked Questions
<> p. 48, section III.1.6.1, a bug in the Lulu pdf generator makes the sort axioms illegible. They should read:
forall n (n=1n ∨ n=2n ∨ n=3n ∨ n=4n ∨ n=5n ∨ n=6n ∨ n=7n ∨ n=8n ∨ n=9n)
forall r (r=1r ∨ r=2r ∨ r=3r ∨ r=4r ∨ r=5r ∨ r=6r ∨ r=7r ∨ r=8r ∨ r=9r)
forall c (c=1c ∨ c=2c ∨ c=3c ∨ c=4c ∨ c=5c ∨ c=6c ∨ c=7c ∨ c=8c ∨ c=9c)
forall b (b=1b ∨ b=2b ∨ b=3b ∨ b=4b ∨ b=5b ∨ b=6b ∨ b=7b ∨ b=8b ∨ b=9b)
forall s (s=1s ∨ s=2s ∨ s=3s ∨ s=4s ∨ s=5s ∨ s=6s ∨ s=7s ∨ s=8s ∨ s=9s)
forall ut (ut=row ∨ ut=col ∨ ut=blk)
<> p. 275 of HLS1, p. 278 of HLS2, there is a typo in the graphical representations of puzzle Sudogen0-456. Thanks to Gordon Fick for signalling it. Digits 4 and 5 avec been interverted in row 5. The correct puzzle, its L1_0 elaboration and its solution shoud read respectively (where 0 stands for an empty cell):
904006000 914506000 914526738
000000501 000900541 263987541
007040000 007041000 857341629
002794100 002794100 382794156
000060090 040860090 741865392
600100804 600100804 695132874
000000000 000000000 126473985
030018000 030018000 539218476
408059200 408059210 478659213
ONLINE SUPPLEMENTS TO THE BOOK
1) General concepts and techniques
2) Techniques for exceptionnally hard puzzles
3) Rating resolution rules and puzzles; classification
4) Additional examples
5) Extension of the techniques developed for Sudoku