Fiendish Sudoku: Brain Teasing Puzzles [M Prefontaine] on *FREE* shipping on qualifying offers. Fiendish Sudoku Book Sudokus are puzzle. Products 1 - 18 of 18 - The Times Fiendish Sudoku found in: The Times Fiendish Su Doku Book 1: Challenging Su Doku Puzzles, The Times Fiendish Su. Angus Johnson's Simple Sudoku web site has a very fine page of Su These are rated in difficulty from mild (the simplest) to fiendish (the one.
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Non-polynomial state space This is where much of the counting appears. This is larger than any fixed power of M this is said to be faster than any polynomial in M. If depth-first enumeration were the only way of counting the number of possible Su Dokus, then this would imply that counting Su Doku is a hard problem.
Application of constraints without clues is the counting problem of Su Fiendish sudoku. As clues are fiendish sudoku in, and the constraints applied, the number of possible states reduces.
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The minimum problem is to find the minimum number of clues which reduces the allowed states to one. The fiendish sudoku problem is analogous.
Many known hard problems are of a type fiendish sudoku nondeterministic-polynomial. In this class, called NP, generating a solution of fiendish sudoku problem of size M takes longer than any fixed power of M, but given a solution, it takes only time of order some fixed power of M to check it ie, a polynomial in M.
If enumeration were the only way of counting the number of Su Doku solutions, then this would be harder than Fiendish sudoku. If someone tells me that the number of Su Doku solutions isI have no way to check this other than by counting, which I know to takes time larger than polynomial in M.
At fiendish sudoku there is no indication that the counting problem of Su Doku is as easy as NP.
The Su Doku problem is to check whether there is fiendish sudoku unique solution to a given puzzle: It is not known whether the Su Doku problem is in NP. One sure fire way of solving any Su Doku puzzle is to forget all these tricks and just blindly do a trial-and-error search, called a depth-first search in fiendish sudoku science.
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When programmed, even pretty sloppily, this can give a solution in a couple of seconds. If trial-and-error were the only algorithm to solve any Su Doku puzzle whatsoever, and one were able to show that the state space of a puzzle grows faster than a fixed power fiendish sudoku M, then this would prove fiendish sudoku Su Doku is an NP problem.
Helmut Simonis has results which might indicate that trial-and-error is never needed, and a small bag of tricks with hyper arc consistency always answers the Su Doku question.
Fiendish sudoku, one needs to ask how many times the consistency check has to be applied to solve the worst-case problem, and how fast this grows with M, in order to decide whether constraint programming simplifies the fiendish sudoku.
The controversy over trial-and-error From this formal point of view, one can see the debate raging currently on Michael Mepham's web fiendish sudoku and other discussion boards on Su Doku as an argument between the search enthusiasts and the constraint programming wallahs: But does the debate just boil down to choosing which algorithm to use?
Yes, if the Su Doku problem is easy ie, in P and constraint programming solves it faster.
Sudoku tips: How to solve Sudoku: The mathematics of Su Doku
However, if Su Doku is hard, then there is a little more to it. Gomes and Selman conjecture that this is due to fiendish sudoku existence of "backdoors", ie, small sets of tricks which solve these average problems. Rule 4 - pairs.
When two squares in the same area row, column or box have identical two-number candidate lists, you can remove both numbers from other candidate lists in that area.
Here's the second row of the puzzle: Two fiendish sudoku the squares have the same candidate list - This means that between them, they will use up the 6 and 7 for this row. That means that the other square can't possibly contain a 6. We can remove the 6 from its candidate list, leaving just 9 - square solved!
The fiendish sudoku in a pair must have exactly two candidates.
If one of the above squares had beenit couldn't have fiendish sudoku part of a pair. Three squares in an area row, column or box form a triple when: