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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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 Posted: Sat Aug 09, 2008 7:59 am Post subject: LA Times/Freep - Aug 8, 2008 |
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| Code: | +-------+-------+-------+
| . . . | . 7 2 | . . . |
| . 9 2 | . . . | 5 7 . |
| . 7 . | 6 . . | . . . |
+-------+-------+-------+
| . . . | . . 1 | 9 . . |
| 6 1 . | . 2 . | . . 3 |
| . . 3 | 9 . . | . 5 . |
+-------+-------+-------+
| . . . | . . 7 | . 4 . |
| . 5 4 | . . . | 8 3 . |
| . . . | 2 3 . | . . . |
+-------+-------+-------+ |
It's not so difficult this week. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sat Aug 09, 2008 10:05 am Post subject: Re: LA Times/Freep - Aug 8, 2008 |
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| Asellus wrote: | | It's not so difficult this week. |
Right. Whole bunch of skyscrapers (7)
But there is also a w-wing:
| Code: |
+--------------------------+--------------------------+--------------------------+
| 13458 3468 1568 | 458 7 2 | 13 9 48 |
| 1348 9 2 | 48 18 38 | 5 7 6 |
| 13458 7 158 | 6 1589 389 | 123 12 48 |
+--------------------------+--------------------------+--------------------------+
| 24578 248 578# | 3 468 1 | 9 26 27* |
| 6 1 9 | 7 2 5 | 4 8 3 |
| 2478 248 3 | 9 468 68 | 267 5 1 |
+--------------------------+--------------------------+--------------------------+
| 123 236 16 | 58 58 7 | 126 4 9 |
| 27* 5 4 | 1 69 69 | 8 3 -27 |
| 9 68 1678# | 2 3 4 | 167 16 5 |
+--------------------------+--------------------------+--------------------------+
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Because of the strong link (7) in col 3, if r4c9 is not 2, then r8c1=2.
This takes out 2 from r8c9.
The other day we talked about how a strong link created by a w-wing must not be taken for a weak link, because both ends might be the same, here is an example: both r4c9 AND r8c1 must be 2. |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Sat Aug 09, 2008 5:35 pm Post subject: Re: LA Times/Freep - Aug 8, 2008 |
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| nataraj wrote: |
But there is also a w-wing ... |
Pretty much the same candidates form an M-wing (primary 3 cells are 27 ), don't they? You can either extend from r8c1 to r9c3 on 7s or from r4c9 to r6c7 on 7s to end up setting all 3 27s.
| Code: | +--------------------------+--------------------------+--------------------------+
| 13458 3468 1568 | 458 7 2 | 13 9 48 |
| 1348 9 2 | 48 18 38 | 5 7 6 |
| 13458 7 158 | 6 1589 389 | 123 12 48 |
+--------------------------+--------------------------+--------------------------+
| 24578 248 578 | 3 468 1 | 9 26 #27 |
| 6 1 9 | 7 2 5 | 4 8 3 |
| 2478 248 3 | 9 468 68 | 267 5 1 |
+--------------------------+--------------------------+--------------------------+
| 123 236 16 | 58 58 7 | 126 4 9 |
|#27 5 4 | 1 69 69 | 8 3 #27 |
| 9 68 1678 | 2 3 4 | 167 16 5 |
+--------------------------+--------------------------+--------------------------+ |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sun Aug 10, 2008 8:17 am Post subject: Re: LA Times/Freep - Aug 8, 2008 |
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| wapati wrote: | Pretty much the same candidates form an M-wing (primary 3 cells are 27 ), don't they? You can either extend from r8c1 to r9c3 on 7s or from r4c9 to r6c7 on 7s to end up setting all 3 27s.
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It is even better than that. In this situation, there is no need to complete the m-wing, because the pair 27 in r4c9 and r8c1, together with a w-wing between those same cells, enable us to solve both pincer cells directly:
A: 27 in r4c9 and r8c1 are connected via 27 in r8c9. By this connection, they are equivalent, i.e. they always have the same solution.
B: 27 in r4c9 and r8c1 are the pincer cells of a w-wing (by way of 7 in col 3). That means, at least one of them must be "2"
A and B taken together, assert that they are both the same and at least one of them must be 2. So both must be "2" 
I saw it yesterday but I did not mention it because I thought it was a very rare "freak" pattern, but as it happened, I solved a "Times" super fiendish this morning (no very hard on this site, alas!) and came across the same pattern.
--------
Edit: Seems to be even more common!
I went looking for a definition of the m-wing when suddenly I came across this post by keith right here on this forum (Sat Jul 12, 2008 9:18 pm in the "A day for easy puzzles?" thread), where he explains this very same logic. I must have overlooked it then ... |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Aug 10, 2008 3:48 pm Post subject: |
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| Quote: | A: 27 in r4c9 and r8c1 are connected via 27 in r8c9. By this connection, they are equivalent, i.e. they always have the same solution.
B: 27 in r4c9 and r8c1 are the pincer cells of a w-wing (by way of 7 in col 3). That means, at least one of them must be "2"
A and B taken together, assert that they are both the same and at least one of them must be 2. So both must be "2" |
Certainly an excellent example of thinking out a solution, something that I never could do. 
Nevertheless, and this is not to denigrate that solution, but, alternatively, for those of us who aren't very good with patterns and deductions, the same can be accomplished via a simple four-cell coloring chain from r8c1 to r6c1.
However, I'm going to try and add that to the arsenal since it probably occurs often enough and doesn't always have that easy coloring alternative, as in the example of puzzle #1981 in another thread. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sun Aug 10, 2008 5:11 pm Post subject: |
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| Marty R. wrote: | | alternatively[...]the same can be accomplished via a simple four-cell coloring chain from r8c1 to r6c1. |
That is true. And the pattern can ALWAYS be viewed as a coloring chain, since only one candidate is used. Interesting, though, that when I found it, my mind was set on "w-wing" and "m-wing" and not coloring at all ...
Last edited by nataraj on Sun Aug 10, 2008 5:49 pm; edited 1 time in total |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Aug 10, 2008 5:35 pm Post subject: |
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| Quote: | | Interesting, though, that when I found it, my mind was set on "w-wing" and "m-wing" and not coloring at all ... |
I think one of the reasons that a given puzzle can have so many solution paths is the fact that different folks have different mindsets plus we each have our own sequence of things we look at. Makes for interesting threads. |
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