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"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.
What's new in the second edition (pdf)
Contents (pdf)
Introduction (pdf)
Conclusion (pdf)
Backcover (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
errata:
<> 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
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