Minimal Puzzles

Everything about Sudoku that doesn't fit in one of the other sections

Postby Mauricio » Sat Oct 13, 2007 8:23 pm

I redid the calculations without the potential hole and found that this pattern is not minimal.
Code: Select all
+-------+-------+-------+
| . . x | x x x | x . . |
| . x x | . . . | x x . |
| x x . | . . . | . x x |
+-------+-------+-------+
| x . . | . . . | . . . |
| x . . | . . . | . . . |
| x . . | . . . | . . . |
+-------+-------+-------+
| . x . | . . . | . . . |
| . x x | . . . | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+


The hole is that I added a few clues (2-4) at a time and then I removed duplicates, but a sudoku morphism that identify 2 isomorphic subpuzzles of that pattern may not be a pattern morphism of the full pattern, and so we would not count some valid puzzles afterwards. In other words, if 2 subpuzzles are isomorphic but the morphism is not a pattern morphism of the full pattern, and we remove the second of them, then we will not be counting some puzzles (offsping of the second one) that could be valid (on the premise that they are isomorphic to a offsping puzzle of the first one, and that could be false).
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Postby JPF » Thu Nov 08, 2007 12:18 am

While Mauricio is looking for some new non minimal patterns, I'd like to raise an open question :

Knowing that a puzzle is minimal, is there any specific techniques to solve it ?

btw, a while ago, I posted this non minimal puzzle :
I wrote:Here is one non minimal puzzle.
x are clues.

Any solvers ?
Code: Select all
 x x 6 | . . . | . . .
 . x . | . . . | 4 . .
 . . . | . . . | . . x
-------+-------+-------
 . . . | x . . | . . .
 . . . | x . x | . . .
 . . . | 9 . . | . x 1
-------+-------+-------
 x . . | . . . | 8 . .
 5 . . | . x . | . . .
 . . . | . 2 . | . 3 .



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Postby RW » Thu Nov 08, 2007 4:14 pm

JPF wrote:Here is one non minimal puzzle.
x are clues.

Any solvers ?
Code: Select all
 x x 6 | . . . | . . .
 . x . | . . . | 4 . .
 . . . | . . . | . . x
-------+-------+-------
 . . . | x . . | . . .
 . . . | x . x | . . .
 . . . | 9 . . | . x 1
-------+-------+-------
 x . . | . . . | 8 . .
 5 . . | . x . | . . .
 . . . | . 2 . | . 3 .


I just spent 10 valuable minutes of my life solving that puzzle, only to find out that Ocean had found the same solution 18 months ago...:(

JPF wrote:Knowing that a puzzle is minimal, is there any specific techniques to solve it ?

This problem is a lot harder than the non minimal puzzle above. I thought about this problem a long time ago when Bill Smythe first proposed it here. If I recall correctly, back then I came to the conclusion that such a technique is impossible...

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Postby JPF » Fri Nov 09, 2007 12:40 am

RW wrote:I just spent 10 valuable minutes of my life solving that puzzle, only to find out that Ocean had found the same solution 18 months ago...:(

Sorry, I should have produced an other puzzle.
I gave it (again) just as an extreme example in this thread of a way to "solve" a puzzle when information on minimality is known.
What would be the conclusions if this information is not given ?

RW wrote:
JPF wrote:Knowing that a puzzle is minimal, is there any specific techniques to solve it ?

This problem is a lot harder than the non minimal puzzle above. I thought about this problem a long time ago when Bill Smythe first proposed it here. If I recall correctly, back then I came to the conclusion that such a technique is impossible...
Could you elaborate please ?

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Postby Mauricio » Thu Nov 22, 2007 10:23 am

JPF wrote:
RW wrote:If I recall correctly, back then I came to the conclusion that such a technique is impossible...
Could you elaborate please ?

JPF

What could such a technique say? Eliminate a candidate? If that is the case, I can't see how adding a candidate and some reasoning would lead us to the conclusion that the puzzle without the added candidate is not minimal, don't you think?
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Postby JPF » Fri Nov 23, 2007 12:46 am

Mauricio wrote:What could such a technique say? Eliminate a candidate? If that is the case, I can't see how adding a candidate and some reasoning would lead us to the conclusion that the puzzle without the added candidate is not minimal, don't you think?

I share your scepticism on such a possible technique.

In addition, if P is the initial (minimal) puzzle, such technique would have to be applied just at the beginning :
as soon as the first cell c is known, P + c is not minimal anymore.

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