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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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 Posted: Tue Feb 19, 2008 2:04 pm Post subject: No Daylight |
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Help !
Earl
| Code: |
+----------+------------+----------+
| 7 5 2 | 189 3 14 | 89 6 48 |
| 19 19 6 | 7 48 45 | 3 2 458 |
| 3 8 4 | 259 29 6 | 59 7 1 |
+----------+------------+----------+
| 26 4 89 | 3 29 7 | 58 1 568 |
| 26 7 89 | 259 1 25 | 4 3 68 |
| 5 3 1 | 4 6 8 | 2 9 7 |
+----------+------------+----------+
| 8 29 7 | 6 5 3 | 1 4 29 |
| 19 6 3 | 128 48 124 | 7 5 29 |
| 4 12 5 | 12 7 9 | 6 8 3 |
+----------+------------+----------+
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Play this puzzle online at the Daily Sudoku site |
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Tue Feb 19, 2008 4:08 pm Post subject: |
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Keith mentioned someone_somewhere and his constellations recently. By coincidence this puzzle responds to a five-star constellation.
While the term eventually came to mean any forcing chain of five links, at least one being strong, someone_somewhere certainly first observed the constellations as a bivalent cell and two strong links on its candidates.
Here the bivalent cell (the alpha star) is r3c7 with candidates (59). The conjugates for 9 in the first row mean that, if the alpha star contains 9, 9 may be eliminated from the rest of the fourth column.
On the other hand, if the alpha star contains 5, the conjugates for 5 in the fourth column mean that r5c4 must contain 5.
So 9 may be eliminated from r5c4.
Steve |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Feb 19, 2008 4:41 pm Post subject: Re: No Daylight |
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| Earl wrote: | Help !
Earl
| Code: |
+----------+------------+----------+
| 7 5 2 | 189 3 14 | 89 6 48 |
| 19 19 6 | 7 48 45 | 3 2 458 |
| 3 8 4 | 259 29 6 | 59 7 1 |
+----------+------------+----------+
| 26 4 89 | 3 29 7 | 58 1 568 |
| 26 7 89 | 259 1 25 | 4 3 68 |
| 5 3 1 | 4 6 8 | 2 9 7 |
+----------+------------+----------+
| 8 29 7 | 6 5 3 | 1 4 29 |
| 19 6 3 | 128 48 124 | 7 5 29 |
| 4 12 5 | 12 7 9 | 6 8 3 |
+----------+------------+----------+
|
Play this puzzle online at the Daily Sudoku site |
I'm very new at this type of thinking, so someone please let me know about this. There is a potential W-Wing on 48 in boxes 2 and 3. There is no obvious strong link connecting them, but I wonder if the 8s in r8c5 and r1c4 form that connection, allowing the 4s to be removed by the pincers in the 48s.
After the above move, I think a similar thing can be done with the 58 pairs in boxes 3 and 6 by using the 8s in r5c9 and r4c3 and that finishes the puzzle.
Last edited by Marty R. on Tue Feb 19, 2008 7:39 pm; edited 2 times in total |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Tue Feb 19, 2008 5:13 pm Post subject: |
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Stars and constellations hm
I am offering a plain old xy-chain and it removes 4 from cells r1c6 r2c9
'48'(r1c9)...r5c9,r5c1,r5c6...'54'(r2c6)
The puzzle is not solved right away.
A little later, more xy-chains are needed but there are like a dozen of them to be found in this position, I've marked a very short one
| Code: |
+--------------------------+--------------------------+--------------------------+
| 7 5 2 | 89 3 1 | 89 6 4 |
| 19 19 6 | 7 48 4-5 | 3 2 58# |
| 3 8 4 | 259 29 6 | 59 7 1 |
+--------------------------+--------------------------+--------------------------+
| 26 4 89 | 3 29 7 | 58 1 568 |
| 26# 7 89 | 259 1 25# | 4 3 68# |
| 5 3 1 | 4 6 8 | 2 9 7 |
+--------------------------+--------------------------+--------------------------+
| 8 29 7 | 6 5 3 | 1 4 29 |
| 19 6 3 | 128 48 24 | 7 5 29 |
| 4 12 5 | 12 7 9 | 6 8 3 |
+--------------------------+--------------------------+--------------------------+
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Stars and constellations - do we really need to travel that far?
To be sure,
That undiscover'd country, from whose bourne
No traveller returns, puzzles the will;
And makes us rather bear those ills we have,
Than fly to others that we know not of? |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Wed Feb 20, 2008 12:04 am Post subject: |
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| Marty wrote: | | I wonder if the 8s in r8c5 and r1c4 form that connection, allowing the 4s to be removed by the pincers in the 48s. |
Sorry, Marty, but those eliminations aren't valid. The <8>s you've selected (in both cases) have the same polarity: either they are both true or they are both false. In order to activate the a W-Wing, they must be strongly linked, which means it must be impossible for both of them to be false. I'm afraid you were lucky this time. |
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Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
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| Posted: Wed Feb 20, 2008 12:55 am Post subject: |
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Medusa coloring on the the alpha star Steve mentioned ends up with the same elimination of <9> in R5C4,(the uncolored <9> in R5C4 can see 9G in R1C3 while
it's own cell contains a R-value) so this earlier constellations may be a precursor of Medusa coloring as we know at the present day?
| Code: | +--------------------------+--------------------------+--------------------------+
| 7 5 2 | 189G 3 14 | 8G9R 6 48 |
| 19 19 6 | 7 48 4G5R | 3 2 45G8 |
| 3 8 4 | 25G9 29 6 | 5R9G 7 1 |
+--------------------------+--------------------------+--------------------------+
| 26 4 89 | 3 29 7 | 5G8R 1 5R68 |
| 26 7 89 | 25R-[9] 1 2R5G | 4 3 68 |
| 5 3 1 | 4 6 8 | 2 9 7 |
+--------------------------+--------------------------+--------------------------+
| 8 29 7 | 6 5 3 | 1 4 29 |
| 19 6 3 | 128 48 12G4 | 7 5 29 |
| 4 12 5 | 12 7 9 | 6 8 3 |
+--------------------------+--------------------------+--------------------------+ |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Wed Feb 20, 2008 1:45 am Post subject: |
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| Asellus wrote: | | Marty wrote: | | I wonder if the 8s in r8c5 and r1c4 form that connection, allowing the 4s to be removed by the pincers in the 48s. |
Sorry, Marty, but those eliminations aren't valid. The <8>s you've selected (in both cases) have the same polarity: either they are both true or they are both false. In order to activate the a W-Wing, they must be strongly linked, which means it must be impossible for both of them to be false. |
Thanks, I always appreciate it when you save me from myself.
| Quote: | | I'm afraid you were lucky this time. |
I guess I should head out and buy some lottery tickets!!! |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Wed Feb 20, 2008 1:48 am Post subject: |
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| Johan wrote: | Medusa coloring on the the alpha star Steve mentioned ends up with the same elimination of <9> in R5C4,(the uncolored <9> in R5C4 can see 9G in R1C3 while it's own cell contains a R-value) so this earlier constellations may be a precursor of Medusa coloring as we know at the present day?
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Steve described this "constellation" as a forcing chain. It is an AIC, which to me is not the same as a forcing chain. In Eureka:
(9)r5c4-(5)r5c4=(5)r3c4-(5=9)r3c7-(9)r1c7=(9)r1c4-(9)r5c4; (9)r5c4<>9
Notice that the AIC requires that the <5>s in c4 and the <9>s in r1 be strongly linked and that they be joined by a bivalue {59}, exactly the requirements of the constellation.
Medusa eliminations can always be accomplished by an AIC. In this particular case the <5>s in r3 and the <9>s in c7 also happen to be strongly linked. That means that the elimination can be accomplished by a single basic Medusa cluster, as you've shown. But, if either or both of those r3 <5>s and c7 <9>s were weakly linked, the constellation elimination would still be valid. However, you would usually need Medusa multi-coloring (two or three "bridged" Medusa clusters) to accomplish the elimination. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Wed Feb 20, 2008 8:53 am Post subject: |
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I remember those 5-star constellations in my early days here, but i never saw a definition. So i just looked at them as 5 cell chains. In this sense there is also a "4-star" here:
| Code: | +----------+------------+----------+
| 7 5 2 | 189 3 14 | 89 6 48 |
| 19 19 6 | 7 48 45 | 3 2 458 |
| 3 8 4 |*259*29 6 | 59 7 1 |
+----------+------------+----------+
| 26 4 89 | 3 *29 7 | 58 1 568 |
| 26 7 89 |*259 1 25 | 4 3 68 |
| 5 3 1 | 4 6 8 | 2 9 7 |
+----------+------------+----------+
| 8 29 7 | 6 5 3 | 1 4 29 |
| 19 6 3 | 128 48 124 | 7 5 29 |
| 4 12 5 | 12 7 9 | 6 8 3 |
+----------+------------+----------+
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r3c4=2 => r6c4=5 => r5c5=9 => r3c5=2
or
r5c4=9 => r3c4=5 => r3c5=2 => r4c5=9
The problem with them is, that they are hard to spot (needing strong links for different colors). They could be everywhere in the puzzle, so where to start looking for them ? |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Wed Feb 20, 2008 9:04 am Post subject: |
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| I like Steve's impressive constellation. But you can, as Nataraj says, do it with XY-chains: 2 did it for me. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Wed Feb 20, 2008 1:35 pm Post subject: |
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I did not try the puzzle before the star discussion had started. But probably i would have found this deadly pattern before looking for any xy- or 5-star-chains:
| Code: | +----------+-------------+------------+
| 7 5 2 | 189 3 14 | 89 6 48 |
|*19*19 6 | 7 48 45 | 3 2 458 |
| 3 8 4 | 259 29 6 | 59 7 1 |
+----------+-------------+------------+
| 26 4 89 | 3 29 7 | 58 1 568 |
| 26 7 89 | 259 1 25 | 4 3 68 |
| 5 3 1 | 4 6 8 | 2 9 7 |
+----------+-------------+------------+
| 8 *29 7 | 6 5 3 | 1 4 *29 |
|*19 6 3 |*128 48 124 | 7 5 *29 |
| 4 *12 5 |*12 7 9 | 6 8 3 |
+----------+-------------+------------+
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=> r8c4=8
Solves with an xy-wing then. |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Wed Feb 20, 2008 3:27 pm Post subject: |
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| That's splendid, Ravel! Wish I could have seen it. |
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