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Marty R.
Joined: 12 Feb 2006 Posts: 5542 Location: Rochester, NY, USA

Posted: Sat Mar 18, 2006 10:41 pm Post subject: Another symetry question 


A month ago I asked a question about a puzzle that seemed asymetrical, but it was pointed out to me that it was, indeed, symetrical. This is the strangest one I've seen yet. It's from the Daily Mail, 318, "Diabolical", but the "Challenging" from the same date seemed just as strange. What gives? If this arrangement is valid (and it must be, I presume, if published by them), why do I see so few of this type?
Code:  
 . . .  8 . .  . . 6 
 1 . .  . 9 .  . . 2 
 . 8 .  . . 7  5 . . 

 9 . 3  6 5 .  . . . 
 . . .  3 . 8  . . . 
 . . 1  . . .  . . . 

 2 9 .  . . .  . 7 . 
 5 . .  2 . .  . . . 
 . . .  . . .  8 . 3 
 


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keith
Joined: 19 Sep 2005 Posts: 3275 Location: near Detroit, Michigan, USA

Posted: Sat Mar 18, 2006 11:17 pm Post subject: Symmetry 


Marty,
This one is asymmetric. There is one block with zero clues, one block with one clue, and one block with two clues. There is no possible symmerty plane that passes through these three blocks.
(Think about it. If there is only one block with N clues, the symmetry plane must pass through that block.)
By the way, I found the puzzle to be fairly easy.
Keith 

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Marty R.
Joined: 12 Feb 2006 Posts: 5542 Location: Rochester, NY, USA

Posted: Sun Mar 19, 2006 5:09 pm Post subject: 


Quote:  By the way, I found the puzzle to be fairly easy. 
I solved it too, with something I found that doesn't even have a name, at least that I've seen. A Jellyfish + 1, i.e., a number confined to five rows in five columns. Then a "Nishio", or some variant thereof, broke it wide open.
It's difficult to assess whatever skill level I might be at, and I still consider myself somewhat of a newbie, but still, when I can solve puzzles graded "Diabolical", "Evil" and the like, I have to think that these gradings are a little overstated. 

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

Posted: Sun Mar 19, 2006 9:50 pm Post subject: 


I've heard the 5x5 fish referred to either as a 'starfish' or a 'squirmbag'. The starfish makes sense, but I'm not sure how the squirmbag worked its way in there.
Last edited by TKiel on Mon Mar 20, 2006 2:25 am; edited 1 time in total 

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keith
Joined: 19 Sep 2005 Posts: 3275 Location: near Detroit, Michigan, USA

Posted: Sun Mar 19, 2006 10:29 pm Post subject: Squirmbag 


Tracy,
Yes, an Xwing is in two rows, a swordfish is in three, a jellyfish is in four, and a squirmbag is in five rows. (Or columns, of course.)
On the programmers' forums I have seen claims that you do not need to write code to find a squirmbag, because then there must also be a jellyfish or lower form. Here is an example comment:
"If squirmbag is just a 5col/row swordfish, then it doesn't exist in a 9x9 sudoku grid. Because Xwing, swordfish, and these other forms are all just a positional form of naked/hidden subsets, a 5column squirmbag is equivalent to a 4row jellyfish, or perhaps a lesser number of rows like 2 or 3 which is more common. This is by the same logic that equates a naked triple in 5 candidates to a hidden pair. If you have only have two of a particular digit locked down, leaving you 7 candidate columns and rows, and a 5column squirmbag exists in those 7, then you can just as easily (actually more easily) find an Xwing in the 2 rows left out of the squirmbag."
(http://www.setbb.com/sudoku/viewtopic.php?t=240)
It sounds reasonable, but I will have to think about it.
Best wishes,
Keith 

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Marty R.
Joined: 12 Feb 2006 Posts: 5542 Location: Rochester, NY, USA

Posted: Mon Mar 20, 2006 1:07 am Post subject: 


Quote:  and a squirmbag is in five rows. 
Thanks. This game isn't lacking in colorful terminology, that's for sure. 

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

Posted: Mon Mar 20, 2006 3:08 am Post subject: 


Keith,
I've read that also, which sorta makes one wonder why a seemingly unnecessary pattern deserves a name at all, much less two . But I know that I have spotted and used them on occasion, before I spotted the lesser fish that was swimming with them.
It's the same reasoning behind not needing to find either a hidden or naked quint.
Marty,
It certainly isn't. Sometimes it would be easier to explain and understand things if there seemed to be a more logical pattern to the names, especially for people who are new to the forum. I remember being confused that an XYwing wasn't some derivation of an Xwing . But discoverers of techniques claim naming rights, which seems to only be fair, so I guess we'll have to live with it. 

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

Posted: Mon Mar 20, 2006 10:52 am Post subject: Symmetry 


Fishy duality is well established. It is also pretty straightforward.
Take an m x m fish based on rows in a square n x n grid. In this base of m rows a particular candidate X can be placed only in the m columns identified by the fish. These are the target columns. The point of the fish is to exclude X from these columns except for the intersections with the base rows.
Now consider the n – m columns which are not target columns. As the Xs in the target columns must lie on the m base rows, the Xs in these other columns must lie on the n – m nonbase rows. Thus there is a dual (n – m) x (n – m) fish for X based on columns and targeting rows.
As long as the grid has square boxes the argument is the same when the fish has fins, bearing in mind that a box is selfdual in this context. (Selfdual in the strict sense: it is not merely that the dual of a box is a box; it is the same box).
I too have seen the proposition that the dual of an m x m fish can be smaller than (n – m) x (n –m) stated as a fact. If anyone knows of an example, I should be very pleased to see it.
Steve 

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keith
Joined: 19 Sep 2005 Posts: 3275 Location: near Detroit, Michigan, USA

Posted: Fri May 19, 2006 1:14 am Post subject: Symmetry 


Marty,
I noticed a post in a different forum on symmetry. Here is an extract:
Quote: 
The symmetry types are enumerated in Gordon Royle's paper here:
http://www.csse.uwa.edu.au/~gordon/sudoku/sudokusymmetry.pdf
In short:
Type I = Full dihedral symmetry
Type II = Full rotational symmetry
Type III = Horizontal and vertical reflection
Type IV = Diagonal and antidiagonal reflection
Type V = 180degree rotational symmetry
Type VI = Horizontal or vertical reflection
Type VII = Diagonal or antidiagonal reflection

Best wishes,
Keith 

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