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sept 19
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Wed Sep 19, 2007 11:04 pm    Post subject: Reply with quote

Kathy,

Here's the "horizontal" Skyscraper on <2>, discussed above, in your grid:
Code:
+---------------+-----------+-------------+
| 2    7    5   | 19 19  6  | 4   8    3  |
| 6    8    9   | 5  4   3  | 2   1    7  |
| 1    3    4   | 2  8   7  | 6   9    5  |
+---------------+-----------+-------------+
| 48  b29   3   | 7  69  45 | 58 B26   1  |
| 5    1    6   | 3  2   8  | 9   7    4  |
| 7    49  #28  | 49 56  1  | 3   56   28 |
+---------------+-----------+-------------+
| 9    45   7   | 8  35  2  | 1   345  6  |
| 348 #245  128 | 6  135 9  | 7   2345 28 |
| 38   6   a128 | 14 7   45 | 58 A235  9  |
+---------------+-----------+-------------+

The parallel strong links are B-b in R4 and A-a in R9. A-B is the middle link since they share C8. (This middle A-B link is "weak" in this case because there are other <2>s in C8.)

As I noted previously, one or both of the pincers "a" and "b" must be true. So <2> is eliminated from the "buddies" of "a" and "b": the cells marked # in this case.

As Earl noted, there is also a "vertical" Skyscraper on <2> in this grid in C2 and C9. You should be able to figure that one out on your own.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Thu Sep 20, 2007 12:01 am    Post subject: Reply with quote

KSipher wrote:
Once again, thanks for the help. I was able to finish the puzzle without needing to use a skyscraper, but I would still appreciate anyone explaining how to apply this method at the point I was stuck at (above.) I would love to add this to my 'skills.' Thanks again!
Kathy


I assume you read Peter's explanation above about the logic. As to how to apply this method, maybe there are different ways. My way is to look for skyscrapers at the same time I'm looking for X-Wings. I check each row and column for two occurrences of a number that will form an X-Wing, but also keep my eyes open for two occurrences that aren't an X-Wing but that do share one line, which is the skyscraper pattern.

Hope this helps.
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nataraj



Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

PostPosted: Thu Sep 20, 2007 5:36 am    Post subject: Reply with quote

Thank you, Asellus and Tracy for the kind explanations. I can see whence the term "color wing" and have also grasped the subtle differences between kite, skyscraper and turbot fish.

Not bad for a start into a new day ...

Regarding solving techniques, I do not believe in using the source of the puzzle as valid information in deciding which steps to try. Unique rectangles are regarded by some as a dubious technique because of the additional piece of information that the puzzle has a unique solution. Well I don't have a problem with that. But "knowing" that The Times super fiendish can always be solved by xwing or swordfish and "knowing" that Dailysudoku.com can always be solved by xy(z) (or whatever) wing and choosing one's route accordingly is going too far for my taste.

When the terrain gets rough, I tend do do a quick search for obvious x-, w- and xy-wings before trying the more time-consuming color wing, xyz, xy chain and medusa coloring as last resort.

I have a nagging feeling that in the end it is more a question of random chance which key move I see first than one or the other technique being superior (as we have learned many times that there are quite a few parallel paths to solution).
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duffy



Joined: 13 Sep 2007
Posts: 26
Location: Toronto Canada

PostPosted: Thu Sep 20, 2007 1:30 pm    Post subject: Reply with quote

I reached Peter's grid copied from his initial post as follows:
+-------------+-----------+------------+
| 2 7 5 | 19 19 6 | 4 8 3 |
| 6 8 9 | 5 4 3 | 2 1 7 |
| 1 3 4 | 2 8 7 | 6 9 5 |
+-------------+-----------+------------+
| 48 29 3 | 7 69 45 | 58 26 1 |
| 5 1 6 | 3 2 8 | 9 7 4 |
| 7 49 28 | 49 56 1 | 3 56 28 |
+-------------+-----------+------------+
| 9 45 7 | 8 35 2 | 1 345 6 |
| 348 245 128 | 6 135 9 | 7 2345 28 |
| 348 6 128 | 14 7 45 | 58 2345 9 |
+-------------+-----------+------------+
I got stuck for a long time on the fascinating pairs in rows 4 and 6: there are three naked triples in 4, and three pairs in 6, but I could not make this delicious finding pay off. After a guess, I uncovered a different FINNED X-WING--I think I have this terminology right--than the one apparently referred to elsewhere: that is, 2's in r4c28, r8c28. The puzzle fell out when I noted, using this wing, that a 2 in r4c8 would dissallow any 2 in box 9, so the 6 in r4c8 breaks the puzzle.
I am describing all this because I could not remember much about a finned x-wing, which leads to a question: Is the finned x-wing a "standard" pattern one should look for?
Question
Don D.
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duffy



Joined: 13 Sep 2007
Posts: 26
Location: Toronto Canada

PostPosted: Thu Sep 20, 2007 3:14 pm    Post subject: Reply with quote

1) Correction: There are two sets of naked triples in row 4. (There is no conjugate hidden pair.)
2) Marty and Tracy: My memory indicates that you both have talked about finned x-wings before, so a word from one of you would be appreciated.
Thanks,
Rolling Eyes
dd.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Thu Sep 20, 2007 4:01 pm    Post subject: Reply with quote

Duffy, this is a writeup I did on the Finned X-Wing.

Code:
+---------+------------+---------+
| 3 68 9  | 7   56  1  | 2 4  58 |
| 7 4  68 | 256 3   25 | 9 1  58 |
| 1 5  2  | 8   4   9  | 6 7  3  |
+---------+------------+---------+
| 2 68 1  | 56  568 4  | 3 9  7  |
| 5 9  3  | 1   26  7  | 8 26 4  |
| 4 7  68 | 9   268 3  | 5 26 1  |
+---------+------------+---------+
| 8 1  4  | 25  9   25 | 7 3  6  |
| 6 2  7  | 3   1   8  | 4 5  9  |
| 9 3  5  | 4   7   6  | 1 8  2  |
+---------+------------+---------+


(This illustrates a Finned X-Wing on 6 in rows 1 and 4.)

Note: this discussion talks about Wings in rows, but the same principles apply to columns.

A Finned X-Wing is an "almost" X-Wing. Let's briefly review the latter. An X-Wing exists when there are two rows which have only two possibilities for a number and the possibilities in each row occupy the same two columns. The number gets eliminated from those two columns in all rows other than the two that are part of the X-Wing. There is an X-Wing pattern on 2 in rows 2 and 7, although there are no eliminations to be made.

A Finned X-Wing exists when one of the rows contains one or two extra occurrences of the number and these occurrences are in the same box as one of the X-Wing cells. The extra occurrences are the "Fins." Note that rows 1 and 4 would contain an X-Wing on 6 in columns 2 and 5 except for the extra 6 (the Fin) in r4c4. So we have an "either-or" situation. There is either an X-Wing or there is not.

For there not to be an X-Wing, r4c4 would have to be = 6, in which case all other 6s would be eliminated from box 5. If there were no 6 in r4c4, then there would be an X-Wing and the 6s would be eliminated from r5c5 and r6c5. The Finned X-wing pattern eliminates these two 6s because they are eliminated regardless of whether there is or is not an X-Wing. To state it slightly differently, the Finned X-Wing eliminates those candidates that would be otherwise eliminated by a regular X-Wing.

The Finned X-Wing occurs fairly often, it can be very powerful and is a valuable part of any player's arsenal.
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Glassman



Joined: 21 Oct 2005
Posts: 50
Location: England

PostPosted: Tue Oct 02, 2007 7:40 am    Post subject: Reply with quote

Marty — Grateful thanks for your explanation of a technique new to me, but not needed here, as I solved this 19 Sept 2007 puzzle using the xy-wing on pivot r9c6 and the skyscraper on 2s (a lovely and logically perfect technique only recently learned). I found this puzzle particularly difficult as the {28} UR, forcing a 1 at r8c3, a defective technique I will not use as it fails to prove the uniqueness of the solution, was so obvious.

This was Sam being really nasty. More please, Sam.

Glassman Cool
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