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20-Hint Puzzle. Hard?

 
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gtong



Joined: 12 Sep 2006
Posts: 3

PostPosted: Tue Sep 12, 2006 6:37 pm    Post subject: 20-Hint Puzzle. Hard? Reply with quote

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 20-hint 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: 3184
Location: near Detroit, Michigan, USA

PostPosted: Tue Sep 12, 2006 9:02 pm    Post subject: Invalid puzzle Reply with quote

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

PostPosted: Tue Sep 12, 2006 10:10 pm    Post subject: 2,671 solutions Reply with quote

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

PostPosted: Wed Sep 13, 2006 2:31 pm    Post subject: Reply with quote

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

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

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

PostPosted: Wed Sep 13, 2006 4:21 pm    Post subject: Reply with quote

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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