View previous topic :: View next topic 
Author 
Message 
Marty R.
Joined: 12 Feb 2006 Posts: 5164 Location: Rochester, NY, USA

Posted: Fri Apr 14, 2006 3:47 pm Post subject: Squirmbag + 1 


I had a 6fish yesterday and was researching to see if it had a name. The Wikipedia entry indicated there's no point in giving it a name in a 9x9 puzzle. Could someone explain that to me? Why would my 6fish be paired with a swordfish? I just don't get it.
"# 5fish : squirmbag  For 9×9 Sudoku, there's no in point naming higherorder (>4) fish, since every Nfish comes paired with a 9N fish whose effect is the same (thus any 5fish is paired with a jellyfish; any 6fish with a swordfish; any 7fish with an xwing; any 8fish with a hidden or naked single). Nevertheless, a 5fish is occasionally called a squirmbag.
# 6+ fish : 6gronk, 7gronk.. [23]  these patterns are only useful for Sudoku larger than 9×9." 

Back to top 


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

Posted: Fri Apr 14, 2006 7:40 pm Post subject: Squirmbag + 1 


Marty, if you still have your 6fish, it should be easy enough to find its dual.
The general scheme is this. Suppose, in an n x n puzzle, you have an m x m fish for X based on rows. The nature of the fish is that it also identifies m columns. These columns are the target columns in the sense that X can be eliminated from the target columns except where they intersect the base rows.
Now think about the other n – m columns, those which are not targets. Where can X be placed? Only outside the base rows. So now we have n – m columns in which X can be placed only in the n – m rows which are not base rows. That is, we have an (n – m) x (n – m) fish based on columns. This is the dual fish. If your 6fish was based on rows, there would be another fish based on the nontarget columns.
This may be a little abstract. Bear in mind that fish are nothing to do with boxes (unless thy have fins); they otherwise relate entirely to columns and rows. So you can permute the columns and rows until a 5fish based on rows looks like this:
Code: 

 X X X X X . . . . 
 X X X X X . . . . 
 X X X X X . . . . 
 X X X X X . . . . 
 X X X X X . . . . 
 . . . . . . . . . 
 . . . . . . . . . 
 . . . . . . . . . 
 . . . . . . . . . 


The fish excludes X from the unmarked cells in columns 1 to 5 so all the Xs in rows 6 to 9 must fall in columns 6 to 9. Marking the possible cells with X gives a 4 fish based on columns 6 to 9:
Code: 

 . . . . . . . . . 
 . . . . . . . . . 
 . . . . . . . . . 
 . . . . . . . . . 
 . . . . . . . . . 
 . . . . . X X X X 
 . . . . . X X X X 
 . . . . . X X X X 
 . . . . . X X X X 


Once the eliminations are made, reverse the permutations and fill in the framework of the boxes to retrieve the puzzle proper.
I have simplified the position a little in an attempt at clarity. Once the principle is grasped, the next stage is to take account of any Xs which have already been inserted in the puzzle. If r Xs have been inserted, the puzzle becomes (n – r) x (n – r) for fishy purposes so the dual of an m x m fish is of dimension (n – r – m) x (n – r – m).
The dual of your 6fish could be a swordfish (no X yet inserted), an XWing (a single X previously entered) or even, in theory, a single square.
Steve 

Back to top 


Marty R.
Joined: 12 Feb 2006 Posts: 5164 Location: Rochester, NY, USA

Posted: Sat Apr 15, 2006 3:59 pm Post subject: 


Steve, thank you very much for taking the time and effort for that explanation.
I don't still have the 6fish. All my puzzles are done with pencil and paper and there's no trail. 

Back to top 




You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot vote in polls in this forum

Powered by phpBB © 2001, 2005 phpBB Group
