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gtong
Joined: 12 Sep 2006 Posts: 3

Posted: Tue Sep 12, 2006 6:37 pm Post subject: 20Hint Puzzle. Hard? 


So I wrote a sudoku puzzle generator and I let it generate some puzzles for me last night. It managed to come up with a few 20hint puzzles. What do you think of the difficulty level? This should be solvable without guessing.
Code: 
++++
 . . .  5 . 7  . . . 
 . 5 .  . 1 .  . 2 . 
 . 6 .  . . .  . . . 
++++
 . . .  4 . 9  3 . . 
 5 7 .  . . .  . . . 
 . . .  . . .  . . . 
++++
 1 . 7  . . 8  . . . 
 . . 9  . . 3  . . 1 
 . 4 .  9 . .  . . 6 
++++

I can post up the other ones if anyone's interested. 

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keith
Joined: 19 Sep 2005 Posts: 3214 Location: near Detroit, Michigan, USA

Posted: Tue Sep 12, 2006 9:02 pm Post subject: Invalid puzzle 


Sudoku Susser solved only four cells. It also pointed out the puzzle has multiple solutions.
Keith 

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David Bryant
Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Posted: Tue Sep 12, 2006 10:10 pm Post subject: 2,671 solutions 


Just FYI, Angus J's "Simple Sudoku" reports 2,671 distinct "solutions" for this puzzle. dcb 

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gtong
Joined: 12 Sep 2006 Posts: 3

Posted: Wed Sep 13, 2006 2:31 pm Post subject: 


So I was discussing this earlier with someone, and my thought was that it's okay for a soduku to have multiple solutions, because it's so easy to verify that you have a solution. I look at it as an excersize in logic, so as long as you can get a solution without guessing, then you've solved the soduku.
His point was that a puzzle should only have 1 solution, which I understand.
I wonder how these programs figure out how many solutions a puzzle has. Maybe I should incorporate that into my own puzzle generator so that it only generates puzzles with 1 solution. 

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David Bryant
Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Posted: Wed Sep 13, 2006 3:00 pm Post subject: If "solution" is not unique, you have to guess 


gtong wrote:  I look at it as an excersize in logic, so as long as you can get a solution without guessing, then you've solved the soduku. ... a puzzle should only have 1 solution, which I understand. 
Hello again, gtong!
Maybe your friend didn't make the point firmly enough. Think about it. If the puzzle has more than one "solution", then it is absolutely impossible to solve it by logic alone. At some point one would have to guess, because at least one cell in the puzzle can contain two different values, meaning that the contents of that cell must be logically indeterminate.
Conversely, if the path through the puzzle is constrained by logical necessity, then there cannot possibly be more than one (unique) solution. Logic is rooted in necessity  "A or not A", and not "maybe A, or maybe not A, or possibly both, or neither".
A "puzzle" that does not have exactly one solution is not a Sudoku puzzle. It's just a 9x9 grid with numbers sprinkled around inside it. dcb 

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gtong
Joined: 12 Sep 2006 Posts: 3

Posted: Wed Sep 13, 2006 4:21 pm Post subject: 


Hm okay I see what you mean. The program kinda guesses, but it's not a real guess. As in, a correct "guess" will allow you to fully solve the puzzle correctly without any more guessing, so it's not really a guess.
Anyway, I'll see what I can do about the algorithm. 

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