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Symetry

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5153
Location: Rochester, NY, USA

PostPosted: Fri Feb 24, 2006 6:44 pm    Post subject: Symetry Reply with quote

I thought all good puzzles were supposed to be symetrical and I had my own ideas of what symetrical was. In the following puzzle (a "pappocom" puzzle) from my local paper today, it seems that boxes 2 and 8 should have the numbers at opposite angles, as in the "2" being up one column and the "7" being down one column. Does this fit the standard meaning of symetrical puzzles?

Code:
-------------
|   |   | 64|
|3 8|4  |  7|
| 5 |  3|8  |
-------------
|   |  5|7 8|
|   |2 1|   |
|9 7|6  |   |
-------------
|  9|7  | 8 |
|6  |  2|5 9|
|48 |   |   |
[/code]
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Fri Feb 24, 2006 10:59 pm    Post subject: Reply with quote

Marty R,

Check out this link http://www.sudoku.com/forums/viewtopic.php?t=3070 for a listing of the many ways a puzzle can be symmetrical.
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keith



Joined: 19 Sep 2005
Posts: 3162
Location: near Detroit, Michigan, USA

PostPosted: Sat Feb 25, 2006 3:26 am    Post subject: The eye of the beholder Reply with quote

Marty,

Most Sudokus are symmetric in their initial grid, but that is just an aesthetic issue. You may notice that crossword puzzle grids are also symmetric?

I think the puzzle you have posted is consistent in its symmmetry (or anti-symmetry) pattern.

The minimum known number of initial squares for a valid Sudoku is 17. I have not seen a symmetric one. I did see a web comment that the minimum symmetric Sudoku has 18 initial squares.

By the way, I have stopped doing the Pappacom puzzles. My current (self-imposed) challenge is to solve the Daily Sudoku with pencil and paper, but with no pencil marks.

Best wishes,

Keith
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sat Feb 25, 2006 6:06 am    Post subject: Reply with quote

Keith,

Just curious as to why you stopped doing the Poppocom puzzles.
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keith



Joined: 19 Sep 2005
Posts: 3162
Location: near Detroit, Michigan, USA

PostPosted: Sat Feb 25, 2006 1:16 pm    Post subject: puzzles Reply with quote

Tracy,

Just a pesonal thing. Most of them are far too easy. I do the David Bodycombe (Detroit Free Press) and the Daily Sudoku, and on most days I try the Dudo Cue Nightmare. Sometimes I solve it!

Keith
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sat Feb 25, 2006 2:06 pm    Post subject: Reply with quote

Keith,

I agree about the lack of difficulty in the Poppacom puzzles in the paper. I think Poppacom's market is the casual Sudoku solver. The local paper runs two V. Easy, two Easy, two Medium and one Hard each week. Having to find nothing more difficult that a naked/hidden triple got boring fast. Now I let my 11 year old daughter do those.
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Marty R.



Joined: 12 Feb 2006
Posts: 5153
Location: Rochester, NY, USA

PostPosted: Sat Feb 25, 2006 7:28 pm    Post subject: Reply with quote

Thanks for the information on symetry.

I'll echo the feelings on the pappocom puzzles. I do them every day because they're there, but even the most difficult, rated as Four-star Hard, are not a big challenge, even for a relative newbie like myself.
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David Bryant



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

PostPosted: Sat Feb 25, 2006 8:04 pm    Post subject: Unusual symmetries Reply with quote

Marty R wrote:
I thought all good puzzles were supposed to be symetrical ...

Most of the published Sudoku puzzles exhibit two-fold rotational symmetry, which can also be visualized as reflection across a diagonal.

This puzzle (Ruud van der Werf's "Nightmare" for last New Year's Eve) exhibits simple bilateral symmetry (reflection across column 5). I guess it's supposed to represent a glass or a goblet with a bubble in it ... pretty good for New Year's, I'd say! dcb
Code:
.........
....7....
6..8.9..3
4...3...9
1.......7
.6.5.1.8.
....9....
..2.5.1..
95.4.2.36
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Sun Feb 26, 2006 5:42 pm    Post subject: Symmetry Reply with quote

Marty

I'm not sure anyone answered your question directly.

If the puzzzle is turned upside down, the pattern is the same. This is 180 degree rotational symmetry.

Steve
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