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ravel · Joined: 21 Apr 2006 Posts: 536

Nice, that also a swordfish is behind there. But its not needed, nor Medusa or another "extended" advanced technique.

storm_norm · Joined: 18 Oct 2007 Posts: 1741

storm_norm · Joined: 18 Oct 2007 Posts: 1741

ok, looking at the grid posted in my previous post...

i found a coloring elimination on 6 taking out a 6 in r2c2.

then an xy-wing pivot in r8c7 {2,3,4}

xyz-wing {5,6,8} r4c3

xy-chain 56-67-78-58, takes out 5 in r1c1

xy-chain 78-67-56-58 takes out 8 in r8c1

xy-chain 67-78-78-67 takes out 6 in r1c2,

I am thinking there is another solution I didn't see?? perhaps some unique eliminations.

Marty R. · Posted: Wed Feb 13, 2008 1:45 am Post subject:

ravel · Joined: 21 Apr 2006 Posts: 536

Victor · Joined: 29 Sep 2005 Posts: 207 Location: NI

Thanks, really nice puzzle!
My solution involved (not in order) X-, XY- & XYZ wings, XY-chain, type 4, skyscraper or other manoevre in 6s, and . .

. . early on, a kite-type elimination of a 6 in r2c2. Here's a small question. One of these things, with the strong links parallel and the weak link at right angles, has been called a Skyscraper. When the weak link is diagonal, in a box, with strong links at right angles, it's been called a Kite. Has this variation, with a strong link diagonally in a box and then the other strong link and the weak link at right-angles, been given a name? (This one has strong links in box 4 & C7, with the connecting weak link in R4.)

(I know you can ask why one should bother naming any of them, but one could equally ask why it's worthwhile in geometry naming different kinds of quadrilateral.)

ravel · Joined: 21 Apr 2006 Posts: 536

Its really a chaos with these names. The first popular name for all these 2 strong link (connected by a weak one) eliminations was turbot fish and nick70 had 4 patterns of them. It was immediately clear, that all eliminations also could be done, when you only look at these connected strong links.
So i liked the name "2 strong links" or 2SL, given by Havard in his Strong Links for Beginners. But it was not commonly used.
The naming of skyscrapers and kites also was not bad, because it describes the pattern. But he did not give the third pattern an own name, where a strong link in a box was connected with one in a line. But i think, most people would call it a kite also.

Also it is hardly mentioned, that these definitions are a bit restrictive, because what i call "grouped strong links" or grouped kite, is essentially the same. And i think Asellus simply calls a grouped kite a kite.
Something like

Asellus · Posted: Wed Feb 13, 2008 11:03 pm Post subject:

ravel,

My understanding of the names is the same as yours. I sometimes use Turbot Fish to refer to those 2SL situations which are not Kites or Skyscrapers. But, the Turbot Fish name is really all inclusive.

And, you are right: I do consider those grouped link situations to be Kites. However, your examples don't seem quite right. The one on the left is a Kite example but is clearer if I add a "~" symbol to indicate a cell that must not contain x. The example on the right is not a Kite; rather, it is an ER elimination, as I see it, and requires that at least one of r6c12 MUST be x:

Victor · Joined: 29 Sep 2005 Posts: 207 Location: NI

Thanks folks: you know your stuff! A final question (don't bother if you've had enough!): is a turbot fish just a 5-pointed loop in one digit, with a discontinuity? - or can it be 7-, 9 -... ? (I know that in general they're called x-cycles, and I think that term is synonymous with fishy cycle, but presumably these terms include even-numbered loops?)

Asellus · Posted: Fri Feb 15, 2008 9:36 pm Post subject:

Victor,

I haven't read up on "loop" and "cycle" terminology. However, if you are referring to a 5-node AIC where one of those nodes (the "victim") is at a 2-weak-link discontinuity then, yes, Turbot Fish conform to that pattern. But, so does the ER elimination above. And I, at least, don't consider an ER to be a Turbot Fish. As I see it, a Turbot Fish requires that the "pincer" cells each be connected by a conjugate link that is in a "straight line". The straight line can be in a row, a column, or between two cells in a box (i.e. "at an angle").

The ER differs in that one "pincer" is a box-line segment that is strongly linked to another box-line segment that is at a right angle to it (i.e., the ER itself). In the example above, the link is strongly inferential if r6c3 (and at least one of r6c12) contains x. It is a grouped conjugate link if r6c12 both contain x and r6c3 does not contain x.

However, that ER diagram does represent what I consider to be a Turbot Fish if, of the cells r6c123, only r6c1 contains x or only r6c2 contains x. In those cases, we have our straight line conjugate link within a box and, thus, our Turbot Fish. (I overlooked pointing this out before.)

Phew! Hope that exhausts this topic.

Victor · Joined: 29 Sep 2005 Posts: 207 Location: NI

Thanks. Promise I won't ask any more silly questions about terminology. Very useful points about grouped kites etc. I suddenly realised myself a few weeks ago that for instance thinking of finned x-wings as they were originally explained is needlessly complicated - much simpler to view them as 'grouped sykscrapers.'
In general, I agree with people who say that the rich sudoku vocabulary is good - why not have some synonyms? A pity though, that sometimes different meanings are assigned to the same word - 'forcing chain' springs to mind.