Between a Y-wing and a turbot fish

Advanced methods and approaches for solving Sudoku puzzles

Between a Y-wing and a turbot fish

Postby 999_Springs » Wed Apr 02, 2008 5:03 pm

Code: Select all
This is a Y-wing:

.  12 . |. . .|-1 -1 -1
.  .  . |. . .|.  .  .
-1 -1 -1|. . .|.  12 .
--------+-----+--------
.  .  . |. . .|.  .  .
.  2--------------2  .
.  .  . |. . .|.  .  .
--------+-----+--------
.  .  . |. . .|.  .  .
.  .  . |. . .|.  .  .
.  .  . |. . .|.  .  .

This is a turbot fish:

.  1  . |. . .|-1 .  -1
.  |  . |. . .|.  .  .
-1 |  -1|. . .|.  1  .
---|----+-----+---|----
.  |  . |. . .|.  |  .
.  1  . |. . .|.  1  .
.  .  . |. . .|.  .  .
--------+-----+--------
.  .  . |. . .|.  .  .
.  .  . |. . .|.  .  .
.  .  . |. . .|.  .  .

So this is somewhere in between...

.  12 . |. . .|-1 .  -1
.  .  . |. . .|.  .  .
-1 -1 -1|. . .|.   1 .
--------+-----+----|---
.  .  . |. . .|.   | .
.  2--------------21 .
.  .  . |. . .|.  .  .
--------+-----+--------
.  .  . |. . .|.  .  .
.  .  . |. . .|.  .  .
.  .  . |. . .|.  .  .

(Note: r5c8 need not be a bivalue cell)

This "thing" halfway between a Y-wing and a turbot fish is formed by replacing one of the bivalue cells in a Y-wing by a strong link as shown in the diagram.
It provides a neat way to solve this puzzle (the first in the "Contrary "17" Puzzles"):

69   1     3   | 4  69 7 | 8 2  5
579  579   4   | 8  59 2 | 6 3  1
2    8     56  | 1  56 3 | 9 4  7
---------------+---------+--------
5679 5679  567 | 57 2  4 | 3 1  8
3    4     2   | 9  1  8 | 7 5  6
8    57    1   | 57 3  6 | 2 9  4
---------------+---------+--------
4    2     9   | 6  7  1 | 5 8  3
67   3     8   | 2  4  5 | 1 67 9
1    567   567 | 3  8  9 | 4 67 2

The bivalue cell is r1c1 and the strong link is in 6s in r49c2. These are connected by means of the strong link in 9s in r4c12. This means that r8c1<>6.
I don't know what this technique is called... but if it is new, I would like a better name than
"Y-wingbot fish" or something like that.
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Once upon a time I was a teenager who was active on here 2007-2011
999_Springs
 
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Postby Steve K » Wed Apr 02, 2008 10:17 pm

I could be the worst person on earth for names. So very many short exactly 3 sis exist. They range from using all hidden sis to using all naked sis, to any combination of hidden and naked sis. The logic for most is really no different than that of a standard xy wing, so I have called them Y Wing Styles - but that is not a good name! Very few mimic the xyz wing, and fewer still a t-chain. Perhaps with 3 sis, one could still name each pattern individually. At 4 sis, the list will get very long.
Steve K
 
Posts: 98
Joined: 18 January 2007

Postby Mike Barker » Thu Apr 03, 2008 2:46 am

This is also a 3-element nice loop. I identified 9 simple types (using bivalues and bilocals) here:
Code: Select all
1) -a-ab-b-bc-c-ca-a-                 continuous => a naked triple, otherwise an XY-wing = Y-wing
2) -a-ab-b-bX=b=bY-b-ab-a-
3) -a-aW=a=aX=b=bY-b-ab-a-
4) -a-aW=a=aX-a-aP=a=aQ-a-aY=a=aZ-a-  continuous => an 222 Swordfish, otherwise a turbot chain
5) -a-aW=a=abX=b=abY=a=aZ-a-          continuous => eliminate X and Y otherwise equivalent to #4
6) -a-aW=a=aX-a-ab-b-ab-a-            equivalent to #4

7) aW=a=aX-a-ab-b-bc~c~aW             eliminate "c" in "aW" only
8) aW=a=abX=b=bY-b-bc~c~aW            eliminate "c" in "aW" only
9) cZ~a~aW=a=abX=b=bcY=c=cZ~c~aW      eliminate "c" in "aW" or "a" in "cZ" only

An XY-wing is the first type and a W-wing was defined to be the second. Your's is the third type. We could name all 9 if that helps people find them or just recognize that they are nice loops. Expanding the list to include grouped nodes or 4 or more element nice loops would probably be untenable.
Mike Barker
 
Posts: 458
Joined: 22 January 2006


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