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Marty R.
Joined: 12 Feb 2006 Posts: 5351 Location: Rochester, NY, USA

Posted: Sun May 21, 2006 5:48 am Post subject: Finned XWing 


I thought I read somewhere that there can be two fins, not just one. Is that correct? I hope I've provided enough information by showing only the "6s" in the relevant boxes. Note that there would be an XWing in r18 and c18 except for the two fins in r1c7 and r1c9. If there was just the one fin, I could conclude that the "6s" in r2c8 and r3c8 must go, but with the two fins, to make the same conclusion, I'd have to conclude that there must be a "6" in r1 of box 3. If that is actually the case, I don't know how to reason that out.
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David Bryant
Joined: 29 Jul 2005 Posts: 559 Location: Denver, Colorado

Posted: Sun May 21, 2006 12:02 pm Post subject: It's a plain vanilla XWing 


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There's an ordinary, every day XWing in rows 3 & 8. So the "6"s at r1c1, r1c8, r2c8, and r7c8 can be eliminated. That leaves r2c3 unique in row 2. dcb 

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keith
Joined: 19 Sep 2005 Posts: 3219 Location: near Detroit, Michigan, USA

Posted: Sun May 21, 2006 2:57 pm Post subject: Fork 


Marty,
Note there is a "fork" in R2 and R3 which eliminates the <6> in R1C1.
Also, you can use coloring to connect R8C8 and R2C3, to eliminate <6> in R2C8.
Keith 

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Marty R.
Joined: 12 Feb 2006 Posts: 5351 Location: Rochester, NY, USA

Posted: Sun May 21, 2006 4:47 pm Post subject: 


"I hope I've provided enough information by showing only the "6s" in the relevant boxes. "
Apparently, I misled. I only showed the "6s" in the boxes where the potential Finned Wing was. There are a few other "6s" floating around, particularly in r3c4. I believe this would preclude both David's XWing and Keith's coloring.
I don't know what a "fork" is.
So my lazy little shortcut backfired. I'm sorry. :oops:
P.S. It's now 15 minutes since I posted the above. I should have searched first. David answered my question on May 4.
Quote:  Well, it's mostly right, Marty. But the "fin" doesn't have to be just one cell ... it can be two cells long. The logic is substantially similar in either case.
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Case A Case B
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..X...X.. ..X...X..
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......*.. ......*..
..X...X#. ..X...X##
......... .........
......... .........
..#...... ..#...... 
A. If r6c8 = "x", then r5c7 <> "x"; if r6c8 <> "x" then XWing on rows exists, and we still have r5c7 <> "x"
B. If r6c8 = "x" or r6c9 = "x", then r5c7 <> "x"; if r6c8 <> "x" and r6c9 <> "x", then XWing on rows exists, and we still have r5c7 <> "x" 
If I understand that correctly, I can eliminate the "6" in r2c8 and r3c8 using similar logic: if either of the fins is true, those "6s" are gone. If neither is true, then an XWing exists and the same two eliminations can be made. I'll proceed with the puzzle on that basis and see where it leads. 

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keith
Joined: 19 Sep 2005 Posts: 3219 Location: near Detroit, Michigan, USA

Posted: Sun May 21, 2006 5:17 pm Post subject: "Fork" 


Marty,
I think you probably know what a "fork" is, but by another name. I posted an explanation in the Saturday puzzle thread:
http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=861
Tracy calls it multicoloring, Havard (in his article on Strong Links) calls it a skyscraper.
Keith 

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Marty R.
Joined: 12 Feb 2006 Posts: 5351 Location: Rochester, NY, USA

Posted: Sun May 21, 2006 9:28 pm Post subject: Re: "Fork" 


Thanks. I know that pattern as "strong links." However, I thought multicoloring was something else. Certainly no shortage of colorful terminology attached to various techniques. 

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ravel
Joined: 21 Apr 2006 Posts: 536

Posted: Mon May 22, 2006 9:48 am Post subject: 


Since i also had mixed the names sometimes:
Strong links are equivalent to advanced coloring.
Multicoloring is a superset (allowing more eliminations), but it is a bit complicated with it to make the eliminations of 3 or more strong links. E.g. for 3 strong links Aa,Bb,Cc i would argue about that:
a and B share a unit => A or b have to be the number x.
b and C share a unit => B or c have to be x.
Since b and B share a unit, also A or c have to be x. 

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Marty R.
Joined: 12 Feb 2006 Posts: 5351 Location: Rochester, NY, USA

Posted: Mon May 22, 2006 3:47 pm Post subject: 


Multicoloring is something I'm going to have to live without, at least for awhile, because I just can't get it to penetrate my thick skull. 

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