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Another symetry question

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5162
Location: Rochester, NY, USA

PostPosted: Sat Mar 18, 2006 10:41 pm    Post subject: Another symetry question Reply with quote

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, 3-18, "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: 3174
Location: near Detroit, Michigan, USA

PostPosted: Sat Mar 18, 2006 11:17 pm    Post subject: Symmetry Reply with quote

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: 5162
Location: Rochester, NY, USA

PostPosted: Sun Mar 19, 2006 5:09 pm    Post subject: Reply with quote

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

PostPosted: Sun Mar 19, 2006 9:50 pm    Post subject: Reply with quote

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: 3174
Location: near Detroit, Michigan, USA

PostPosted: Sun Mar 19, 2006 10:29 pm    Post subject: Squirmbag Reply with quote

Tracy,

Yes, an X-wing 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 5-col/row swordfish, then it doesn't exist in a 9x9 sudoku grid. Because X-wing, swordfish, and these other forms are all just a positional form of naked/hidden subsets, a 5-column squirmbag is equivalent to a 4-row 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 5-column squirmbag exists in those 7, then you can just as easily (actually more easily) find an X-wing 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: 5162
Location: Rochester, NY, USA

PostPosted: Mon Mar 20, 2006 1:07 am    Post subject: Reply with quote

Quote:
and a squirmbag is in five rows.


Thanks. This game isn't lacking in colorful terminology, that's for sure. Exclamation
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TKiel



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

PostPosted: Mon Mar 20, 2006 3:08 am    Post subject: Reply with quote

Keith,

I've read that also, which sorta makes one wonder why a seemingly unnecessary pattern deserves a name at all, much less two Question. 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 XY-wing wasn't some derivation of an X-wing Embarassed. 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

PostPosted: Mon Mar 20, 2006 10:52 am    Post subject: Symmetry Reply with quote

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 non-base 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 self-dual in this context. (Self-dual 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: 3174
Location: near Detroit, Michigan, USA

PostPosted: Fri May 19, 2006 1:14 am    Post subject: Symmetry Reply with quote

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/sudoku-symmetry.pdf

In short:
Type I = Full dihedral symmetry

Type II = Full rotational symmetry

Type III = Horizontal and vertical reflection

Type IV = Diagonal and anti-diagonal reflection

Type V = 180-degree rotational symmetry

Type VI = Horizontal or vertical reflection

Type VII = Diagonal or anti-diagonal reflection


Best wishes,

Keith
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