Most of the Puzzles cannot be solved by logic alone some guesswork is needed. In other words, the puzzles are incomplete if the idea is to solve by logic alone!
Posted by
Ranjit
on August 11, 2005 at 05:51 AM PDT
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Hi Ranjit - not so, every puzzle here can be solved using only the rules I've described (elimination, uniques, pairs/triples/quads, etc.) -- no guessing required!
Posted by
Dan Rice
on August 11, 2005 at 02:55 PM PDT
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Hi Dan( Rice),
All the rules y've described are very interesting .
I feel they are not coming only from observations.
What's the mathematical theory under them . Group theory. Another one ?
I hope you have other ideas to share with us
Thank you for your expertise.
Francois
Posted by
siocnarftenurb@videotron.ca
on August 11, 2005 at 07:18 PM PDT
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Hi Francois - Sudoku can be viewed as a simple problem in graph coloring, which is part of a field called graph theory. I'll say more about graph coloring soon.
I doubt group theory would be helpful since the elements in Sudoku never interact with each other. Group theory is all about how elements of a group interact with each other, in ways that are similar to addition and multiplication of numbers.
Posted by
Dan Rice
on August 12, 2005 at 07:46 AM PDT
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Many puzzles are hard enough that they will require guesswork.
Posted by
Paul
on September 04, 2005 at 03:25 PM PDT
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Is it guesswork or simply a more comlicated example of ruling out possibilities?
In mathematics proofs are occasionally achieved through "reductio ad absurdem" - you assume something which leads to a logical inconsistency or invalid result, thus proving the assumption is false.
Posted by
Jack Lubek
on September 17, 2005 at 03:05 PM PDT
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Isn't "reductio ad absurdem" just a fancy way of saying guess and check? i could be wrong, but it sounds like you're just taking a guess and if it's wrong, you try something else... and if it's correct then, yay!
Posted by
Erica
on October 06, 2005 at 10:41 AM PDT
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No it isn't. If you want to prove that A is true you assume it isn't and apply logic to reach an inconsistency. Then you conclude that A must be true after all. You do not go and try B and then C ... That would be guessing.
Posted by
Javier
on October 20, 2005 at 10:50 AM PDT
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Proof by contradiction.
Posted by
joe
on November 19, 2005 at 08:54 PM PST
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Dan R. Your asumption about groups is samewhat wrong in how you stated it, group theory looks at how elements from groups under defined operations. The operations are not limited to purely mathmatical operations either. The Rubix Cube for example is actualy a group. The operation is one of physical moves that changes the position of the elements in other areas. For Soduku, the operation is assigning an element N to some location ij where effect on the rest of the grid is one of exclusion in the common row and column or nonet. So every move you make does interact with the other element.
Now as to wether or not Soduku forms a group or not is yet to be determined, but im working on it. If it does form a group then in theory a common solution could be found to all Soduku puzzles, though it could be more complex than just asigning the normal logic of exclusion.
Posted by
westond
on May 28, 2006 at 02:21 PM PDT
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Posted by Ranjit on August 11, 2005 at 05:51 AM PDT #
Posted by Dan Rice on August 11, 2005 at 02:55 PM PDT #
Posted by siocnarftenurb@videotron.ca on August 11, 2005 at 07:18 PM PDT #
Posted by Dan Rice on August 12, 2005 at 07:46 AM PDT #
Posted by Paul on September 04, 2005 at 03:25 PM PDT #
Posted by Jack Lubek on September 17, 2005 at 03:05 PM PDT #
Posted by Erica on October 06, 2005 at 10:41 AM PDT #
Posted by Javier on October 20, 2005 at 10:50 AM PDT #
Posted by joe on November 19, 2005 at 08:54 PM PST #
Posted by westond on May 28, 2006 at 02:21 PM PDT #