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Finned X-Wing

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5121
Location: Rochester, NY, USA

PostPosted: Sun May 21, 2006 5:48 am    Post subject: Finned X-Wing Reply with quote

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 X-Wing 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.

Code:
-------------
|6--|---|666|
|--6|---|-6-|
|6--|---|-6-|
-------------
|---|---|---|
|---|---|---|
|---|---|---|
-------------
|--6|---|-66|
|6--|---|-6-|
|---|---|---|
-------------
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Sun May 21, 2006 12:02 pm    Post subject: It's a plain vanilla X-Wing Reply with quote

Code:
-------------
|6--|---|666|
|--6|---|-6-|
|6--|---|-6-|
-------------
|---|---|---|
|---|---|---|
|---|---|---|
-------------
|--6|---|-66|
|6--|---|-6-|
|---|---|---|
-------------

There's an ordinary, every day X-Wing 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: 3150
Location: near Detroit, Michigan, USA

PostPosted: Sun May 21, 2006 2:57 pm    Post subject: Fork Reply with quote

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: 5121
Location: Rochester, NY, USA

PostPosted: Sun May 21, 2006 4:47 pm    Post subject: Reply with quote

"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 X-Wing 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.
Code:
Case A Case B
Code:
.........   .........
..X...X..   ..X...X..
.........   .........
.........   .........
......*..   ......*..
..X...X#.   ..X...X##
.........   .........
.........   .........
..#......   ..#......


A. If r6c8 = "x", then r5c7 <> "x"; if r6c8 <> "x" then X-Wing 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 X-Wing 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 X-Wing 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: 3150
Location: near Detroit, Michigan, USA

PostPosted: Sun May 21, 2006 5:17 pm    Post subject: "Fork" Reply with quote

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 multi-coloring, Havard (in his article on Strong Links) calls it a skyscraper.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5121
Location: Rochester, NY, USA

PostPosted: Sun May 21, 2006 9:28 pm    Post subject: Re: "Fork" Reply with quote

keith wrote:
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 multi-coloring, Havard (in his article on Strong Links) calls it a skyscraper.

Keith

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



Joined: 21 Apr 2006
Posts: 536

PostPosted: Mon May 22, 2006 9:48 am    Post subject: Reply with quote

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 A-a,B-b,C-c 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: 5121
Location: Rochester, NY, USA

PostPosted: Mon May 22, 2006 3:47 pm    Post subject: Reply with quote

Multi-coloring 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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