Fully symmetrical puzzles

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

Postby RW » Thu Aug 09, 2007 6:43 pm

Are there any known minimal fully symmetrical puzzles with >32 clues yet? Guess there could be some lurking in the vast amount of 36s generated lately...

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Postby Mauricio » Sat Aug 18, 2007 8:59 am

RW wrote:Are there any known minimal fully symmetrical puzzles with >32 clues yet?

Are there (absolutely) minimal fully simmetryc puzzles with 32 clues?
I scanned this thread and it seems that all puzzles posted with >=32 clues are not minimal.

Now just some contribution of mine, I was thinking about posting some of these in the patterns game thread, but IMO they are overkill (as the rules require the puzzles to be minimal, and it was not easy to generate them).
Code: Select all
#28 clues, minimal
+-------+-------+-------+
| . . 1 | . 2 . | 3 . . |
| . 3 . | 1 . 4 | . 5 . |
| 6 . 4 | . . . | 2 . 1 |
+-------+-------+-------+
| . 1 . | . . . | . 7 . |
| 8 . . | . . . | . . 9 |
| . 2 . | . . . | . 6 . |
+-------+-------+-------+
| 3 . 6 | . . . | 7 . 5 |
| . 4 . | 3 . 6 | . 8 . |
| . . 8 | . 7 . | 4 . . |
+-------+-------+-------+

Code: Select all
#29 clues, minimal
+-------+-------+-------+
| . . 1 | . 2 . | 3 . . |
| . 2 . | 1 . 4 | . 5 . |
| 6 . 3 | . . . | 2 . 1 |
+-------+-------+-------+
| . 3 . | . . . | . 7 . |
| 4 . . | . 5 . | . . 3 |
| . 8 . | . . . | . 6 . |
+-------+-------+-------+
| 7 . 8 | . . . | 6 . 5 |
| . 6 . | 5 . 1 | . 3 . |
| . . 4 | . 7 . | 9 . . |
+-------+-------+-------+
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Postby ravel » Sat Aug 18, 2007 6:00 pm

Nice, maybe also an idea for a very different pattern game (but i will be on holidays after next week).

Is there a tool out there to scan puzzles for symmetry ? I dont have any time to program it myself now.
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Postby Pat » Sun Aug 19, 2007 8:54 am

ravel wrote:Is there a tool out there to scan puzzles for symmetry ?

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ab (2006.Mar.6) -- 29 clues

Postby Pat » Mon Aug 20, 2007 10:25 am

ab (2006.Mar.6) wrote:
      [ 29 clues ]
Code: Select all
 1 4 . . 2 . . 9 8
 6 . . 7 . 4 . . 3
 . . 5 . . . 2 . .
 . 9 . . . . . 5 .
 3 . . . 6 . . . 7
 . 2 . . . . . 6 .
 . . 9 . . . 7 . .
 8 . . 3 . 2 . . 6
 2 7 . . 4 . . 8 5



and several more fully-symmetrical puzzles
follow in that Topic
    edit: i now see that JPF (2006.Apr.17 -- in the first page of the present Topic)
    had already quoted one of the puzzles in that Topic
Last edited by Pat on Sun Aug 26, 2007 9:01 am, edited 1 time in total.
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the "Pure X-Wing Collection" -- fully-symmetrical

Postby Pat » Mon Aug 20, 2007 10:43 am

Ocean (2006.Apr.28) wrote:
      A Pure X-Wing Collection

      For the esthetics,
      the puzzles are minimal,
      and have full symmetry (rotation and reflection).

      [ 7 puzzles, 24 clues ]
Code: Select all
...1.6.....4...3...9.8.2.5.2.5...7.9.........3.8...1.6.1.4.5.2...2...5.....6.8...
..8...2.....537...5.......1.1..4..7..9.2.3.1..2..6..4.1.......6...428.....9...4..
5...8...3.7.9.6.8...4...7...2.....1.8.......5.5.....3...2...9...6.7.5.2.4...3...7
...8.4....3..1..6...7...9..7...3...4.9.7.2.1.4...9...2..5...6...1..5..7....9.3...
..89.52......4....1.......94...7...1.7.6.1.9.9...2...37.......5....1......64.89..
..........62...18..9.5.1.3...73.82.............64.75...5.7.4.9..23...86..........
....6......9.7.8...4.2.8.5...7...5..96.....12..2...9...3.9.1.4...8.5.3......8....



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Postby ravel » Mon Aug 20, 2007 10:49 am

Pat wrote:-eS==8

Thanks, but this option only filters out puzzles, which already are fully symmetrical. I would need a tool that determines, if there is a symmetrical equivalent to a given puzzle (this should not be a very time consuming job).
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Postby Pat » Mon Aug 20, 2007 11:14 am

ravel wrote:
Pat wrote:-eS==8

Thanks, but this option only filters out puzzles, which already are fully symmetrical.

I would need a tool that determines, if there is a symmetrical equivalent to a given puzzle (this should not be a very time consuming job).



Grid symmetrized to largest dihedral order,
"assymmetric" if no symmetry
(not a fast implementation).
    -f%#sc
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Postby ravel » Mon Aug 20, 2007 11:26 am

Thanks again, better slow than nothing:)
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re: a tool to scan puzzles for symmetry

Postby Pat » Mon Aug 20, 2007 1:19 pm

      this looks promising,
      but i haven't tried --
        -esymmetrize()==8
      (perhaps combined with the above -f ?)
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The Times (2007.Aug.16) -- 29 clues

Postby Pat » Mon Aug 20, 2007 1:23 pm

The Times (2007.Aug.16) wrote:
      [ 29 clues ]
Code: Select all
 . . . . 7 . . . .
 . . 5 4 . 8 7 . .
 . 7 . 2 . 3 . 9 .
 . 8 1 . . . 2 4 .
 4 . . . 8 . . . 7
 . 5 7 . . . 8 1 .
 . 4 . 7 . 5 . 6 .
 . . 8 6 . 2 5 . .
 . . . . 1 . . . .


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Postby ravel » Mon Aug 20, 2007 6:15 pm

The only symmetry i found in more than 10000 minimal 36's is this rotational symmetry:
Code: Select all
 +-------+-------+-------+
 | . . . | 4 . 6 | . 8 . |
 | 4 . . | . . . | 2 . 6 |
 | 9 . 8 | 3 . 2 | . 5 4 |
 +-------+-------+-------+
 | 5 . 6 | 9 . 3 | . 7 8 |
 | . . . | . . . | . . . |
 | 8 9 . | 7 . 5 | 6 . 3 |
 +-------+-------+-------+
 | 6 4 . | 5 . 7 | 8 . 2 |
 | 2 . 5 | . . . | . . 7 |
 | . 8 . | 2 . 4 | . . . |
 +-------+-------+-------+

There was no symmetry at all in almost 8000 37's (most of them derived from Havard's 38's).
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Postby Pat » Wed Aug 22, 2007 9:07 am

ravel wrote:There was no symmetry at all in almost 8000 37s
(most of them derived from Havard's 38s)


my understanding is that Håvard's minimal 38s were derived from circa 100,000 minimal 37s -- perhaps we should ask him to search these 37s for symmetry? or is it obvious that no symmetry will be found there??
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Postby Havard » Wed Aug 22, 2007 1:18 pm

Pat wrote:
ravel wrote:There was no symmetry at all in almost 8000 37s
(most of them derived from Havard's 38s)


my understanding is that Håvard's minimal 38s were derived from circa 100,000 minimal 37s -- perhaps we should ask him to search these 37s for symmetry? or is it obvious that no symmetry will be found there??


When I get a bit of time, I will compile a list of all known 37's, and make that available.:)

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Postby Mauricio » Sun Aug 26, 2007 9:37 am

Is this the first known minimal fully symmetrical sudoku with 32 clues?
Code: Select all
#32 clues, abs. minimal
+-------+-------+-------+
| . . . | . . . | . . . |
| . 1 2 | 3 4 5 | 6 7 . |
| . 3 . | . 1 . | . 2 . |
+-------+-------+-------+
| . 2 . | . 7 . | . 1 . |
| . 6 1 | 4 . 3 | 2 5 . |
| . 5 . | . 6 . | . 4 . |
+-------+-------+-------+
| . 4 . | . 5 . | . 6 . |
| . 7 5 | 1 3 6 | 4 8 . |
| . . . | . . . | . . . |
+-------+-------+-------+

Isomorphic pattern, non isomorphic puzzle.
Code: Select all
#32 clues, abs. minimal
+-------+-------+-------+
| . . . | . . . | . . . |
| . . 1 | . 2 . | 3 . . |
| . 2 3 | 1 4 5 | 6 7 . |
+-------+-------+-------+
| . . 2 | . 3 . | 7 . . |
| . 7 5 | 2 . 4 | 1 3 . |
| . . 4 | . 1 . | 5 . . |
+-------+-------+-------+
| . 4 7 | 3 6 2 | 8 5 . |
| . . 6 | . 5 . | 4 . . |
| . . . | . . . | . . . |
+-------+-------+-------+
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