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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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 Posted: Sat May 17, 2008 6:24 pm Post subject: competition #1041 |
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| Code: | . . 1|7 . 6|5 . .
. 4 .|. 2 5|. . 9
. . 6|. . .|. . .
-----+-----+-----
. . .|. 7 3|. 5 .
. . 3|1 . .|6 . .
. 5 .|9 8 .|. . .
-----+-----+-----
. . .|. . .|4 . .
2 . .|. . .|. 3 .
. . 4|8 . 7|9 . . |
the friday diabolical from sudokulist.
couple paths to take. either look for a few xy-chains, which will lead you to a xy-wing to solve it. or go with a couple UR's at the beginning, then the xyz-wing in box 5, but you still would need a couple xy-chains. I couldn't find a massively damaging move.
| Code: | .---------------------.---------------------.---------------------.
| 3 2 1 | 7 9 6 | 5 48 48 |
| 78 4 78 | 3 2 5 | 1 6 9 |
| 5 9 6 | 4 1 8 | 23 7 23 |
:---------------------+---------------------+---------------------:
| 489 1 289 | 6 7 3 | 28 5 248 |
| 478 78 3 | 1 5 24 | 6 9 2478 |
| 6 5 27 | 9 8 24 | 237 14 12347 |
:---------------------+---------------------+---------------------:
| 789 3678 5 | 2 36 19 | 4 18 1678 |
| 2 678 789 | 5 4 19 | 78 3 1678 |
| 1 36 4 | 8 36 7 | 9 2 5 |
'---------------------'---------------------'---------------------' |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat May 17, 2008 7:46 pm Post subject: |
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After the UR's and a few (XYZ, XY) -wings I get here:
| Code: | +-------------+-------------+-------------+
| 3 2 1 | 7 9 6 | 5 48 48 |
| 78 4 78 | 3 2 5 | 1 6 9 |
| 5 9 6 | 4 1 8 | 2 7 3 |
+-------------+-------------+-------------+
| 49 1 29a | 6 7 3 | 8 5 24 |
| 478 -78 3 | 1 5 24 | 6 9 247 |
| 6 5 27b | 9 8 24 | 3 14 147 |
+-------------+-------------+-------------+
| 789 78d 5 | 2 3 19 | 4 18 6 |
| 2 6 89c | 5 4 19 | 7 3 18 |
| 1 3 4 | 8 6 7 | 9 2 5 |
+-------------+-------------+-------------+ |
Here an extended XY-wing argument:
Note the cells a and b. They sort of act like a cell <79> in B4 or C3. Now, consider the XY-wing d-c-ab.
If c is <8>, d is <7>.
If c is <9>, b is <7>.
Any cell that sees both b and d cannot be <7>, solving R5C2.
There is one more XY-wing, and the puzzle is solved.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat May 17, 2008 9:03 pm Post subject: |
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| Code: | | 3 2 1 | 7 9 6 | 5 48 48 |
| 78 4 78 | 3 2 5 | 1 6 9 |
| 5 9 6 | 4 1 8 | 2 7 3 |
+-------------+-------------+-------------+
| 49 1 29a | 6 7 3 | 8 5 24 |
| 478 -78 3 | 1 5 24 | 6 9 247 |
| 6 5 27b | 9 8 24 | 3 14 147 |
+-------------+-------------+-------------+
| 789 78d 5 | 2 3 19 | 4 18 6 |
| 2 6 89c | 5 4 19 | 7 3 18 |
| 1 3 4 | 8 6 7 | 9 2 5 |
+-------------+-------------+-------------+ |
Alternatively, the W-Wing on 78 in boxes 1 and 7 also kills off the 7 in r5c2. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat May 17, 2008 9:27 pm Post subject: |
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| Marty R. wrote: |
Alternatively, the W-Wing on 78 in boxes 1 and 7 also kills off the 7 in r5c2. |
Marty,
I don't see it.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun May 18, 2008 12:36 am Post subject: |
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| keith wrote: | | Marty R. wrote: |
Alternatively, the W-Wing on 78 in boxes 1 and 7 also kills off the 7 in r5c2. |
Marty,
I don't see it.
Keith |
Keith, they're connected by the 8s in column 3.
P.S. Just noticed the W-Wing on 78 in boxes 1 and 4, connected by the 7s in column 3, which also does the same thing. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun May 18, 2008 1:55 am Post subject: |
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Marty,
Aha!
Can't believe I stared at those <78> cells for so long, and did not see the W-wings. I was looking for them!
Keith |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sun May 18, 2008 3:25 am Post subject: |
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| Marty R. wrote: | | keith wrote: | | Marty R. wrote: |
Alternatively, the W-Wing on 78 in boxes 1 and 7 also kills off the 7 in r5c2. |
Marty,
I don't see it.
Keith |
Keith, they're connected by the 8s in column 3.
P.S. Just noticed the W-Wing on 78 in boxes 1 and 4, connected by the 7s in column 3, which also does the same thing. |
hate to spoil the party, but I am not sure that the 7 in r5c2 is eliminated from any w-wings. I see the xy-chain that Keith used to eliminate it, but not from any w-wings.
from Keith's grid.
the above image shows the W-wing on {7,8} with strong links in col 3 as Marty pointed out, but the 7's do not eliminate the 7 in r5c2, it eliminates the 7 in r7c1.
there is the same elimination if you use the strong link on 8 in row 5 with the same {7,8} pair.
here are the w-wing using 7 as a strong link thus eliminating 8's.
Last edited by storm_norm on Sun May 18, 2008 3:44 am; 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 May 18, 2008 3:44 am Post subject: |
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| Quote: | | Can't believe I stared at those <78> cells for so long, and did not see the W-wings. I was looking for them! |
You've now been given a valuable insight into what it's like to be me. 
| Quote: | | the above image shows the W-wing on {7,8} with strong links in col 3 as Marty pointed out, but the 7's do not eliminate the 7 in r5c2, it eliminates the 7 in r7c1 |
Norm, I guess I could have been more clear. Zapping the 7 from r7c1 creates an 89 pair in box 7 which leads to the elimination of the 7 in r5c2. The other W-Wing, which has 8 as pincers, eliminates the 8 from r5c1, leaving r5c2 as the only remaining 8 in box 4.
So both W-Wings lead to the same elimination as Keith's far-more-clever XY-Wing. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sun May 18, 2008 3:58 am Post subject: |
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| Quote: | | Norm, I guess I could have been more clear. Zapping the 7 from r7c1 creates an 89 pair in box 7 which leads to the elimination of the 7 in r5c2. The other W-Wing, which has 8 as pincers, eliminates the 8 from r5c1, leaving r5c2 as the only remaining 8 in box 4. |
thank you, I didn't realize the intermediate steps. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun May 18, 2008 4:35 am Post subject: |
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You can also use the <27> <29> pair ab as the pivot of an XY-wing: Along with c <89> and R5C2 <78> the XY-wing eliminates <8> in cell d.
Same result as the elimination I pointed out before.
If you happen to see an XY-wing as a three-link XY-chain, this extended XY-wing is a four-link chain. But, you collapse one of the links.
Keith |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Mon May 19, 2008 8:20 am Post subject: |
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Hi, dont have time for sudoku these weeks, but i see, that all i could say is already known here 
Just a quick comment to the extended xy-wing.
| keith wrote: | | Code: | +-------------+-------------+-------------+
| 3 2 1 | 7 9 6 | 5 48 48 |
| 78 4 78 | 3 2 5 | 1 6 9 |
| 5 9 6 | 4 1 8 | 2 7 3 |
+-------------+-------------+-------------+
| 49 1 29a | 6 7 3 | 8 5 24 |
| 478 -78 3 | 1 5 24 | 6 9 247 |
| 6 5 27b | 9 8 24 | 3 14 147 |
+-------------+-------------+-------------+
| 789 78d 5 | 2 3 19 | 4 18 6 |
| 2 6 89c | 5 4 19 | 7 3 18 |
| 1 3 4 | 8 6 7 | 9 2 5 |
+-------------+-------------+-------------+ |
Here an extended XY-wing argument:
Note the cells a and b. They sort of act like a cell <79> in B4 or C3. Now, consider the XY-wing d-c-ab ... |
The way i see it, a (29) and c (89) form the pivot. Since these are the only 9's in c3, either a is 2 (and b is 7) or c is 8 (and d is 7).
a and b are a potential extended xy-wing pivot (a is 9 or b is 7), but dont have appropriate pincers. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon May 19, 2008 9:50 am Post subject: |
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| ravel wrote: | Hi, dont have time for sudoku these weeks, but i see, that all i could say is already known here
Just a quick comment to the extended xy-wing.
a and b are a potential extended xy-wing pivot (a is 9 or b is 7), but dont have appropriate pincers. |
| Code: | +-------------+-------------+-------------+
| 3 2 1 | 7 9 6 | 5 48 48 |
| 78 4 78 | 3 2 5 | 1 6 9 |
| 5 9 6 | 4 1 8 | 2 7 3 |
+-------------+-------------+-------------+
| 49 1 29a | 6 7 3 | 8 5 24 |
| 478 78e 3 | 1 5 24 | 6 9 247 |
| 6 5 27b | 9 8 24 | 3 14 147 |
+-------------+-------------+-------------+
| 789 78d 5 | 2 3 19 | 4 18 6 |
| 2 6 89c | 5 4 19 | 7 3 18 |
| 1 3 4 | 8 6 7 | 9 2 5 |
+-------------+-------------+-------------+ |
If ab <79> is the pivot, then surely e <78> and c <89> are pincers, taking out <8> in d?
Keith |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Mon May 19, 2008 10:18 am Post subject: |
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Yes, of course, how could i miss that ?
Must be out of practice |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Mon May 19, 2008 7:50 pm Post subject: |
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| Bit confused here by the references to plural UR's. I got much further than Storm Norm's grid using basics (there was a quad in there somewhere). I then used the <36> UR in R79 that leaves <78> in R7C2. But I cannot see any other URs. |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Mon May 19, 2008 8:28 pm Post subject: |
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..... if it helps - this is as far as I got:
| Code: |
+-----------+---------+--------------+
| 3 2 1 | 7 9 6 | 5 48 48 |
| 78 4 78 | 3 2 5 | 1 6 9 |
| 5 9 6 | 4 1 8 | 23 7 23 |
+---------+-----------+--------------+
| 489 1 289| 6 7 3 | 28 5 248 |
| 478 78 3 | 1 5 24 | 6 9 2478|
| 6 5 27 | 9 8 24 | 237 14 12347|
+-----------+---------+--------------+
| 789 78 5 | 2 3 19 | 4 18 6 |
| 2 6 89 | 5 4 19 | 78 3 178|
| 1 3 4 | 8 6 7 | 9 2 5 |
+-----------+----------+-------------+
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon May 19, 2008 8:48 pm Post subject: |
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Here is where you run out of basics:
| Code: | +-------------------+-------------------+-------------------+
| 3 2 1 | 7 9 6 | 5 48 48 |
| 78 4 78 | 3 2 5 | 1 6 9 |
| 5 9 6 | 4 1 8 | 23 7 23 |
+-------------------+-------------------+-------------------+
| 489 1 289 | 6 7 3 | 28 5 248 |
| 478 78 3 | 1 5 24 | 6 9 2478 |
| 6 5 27 | 9 8 24 | 237 14 12347 |
+-------------------+-------------------+-------------------+
| 789 3678 5 | 2 36 19 | 4 18 1678 |
| 2 678 789 | 5 4 19 | 78 3 1678 |
| 1 36 4 | 8 36 7 | 9 2 5 |
+-------------------+-------------------+-------------------+ |
There is a UR <23> in R36C79, and another <36> in R79C25.
The XYZ-wing is <248> in R4C9.
Keith |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Mon May 19, 2008 10:00 pm Post subject: |
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Keith: Still confused because I had already found the UR in <36> R79C25 (as per my post). But looking at your grid I still can't see the
UR <23> in R36C79.
Craig |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon May 19, 2008 11:52 pm Post subject: |
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| Just thought I'd point out that those "extended XY Wings" are 1-cell and 3-cell ALS eliminations. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue May 20, 2008 12:21 am Post subject: |
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| cgordon wrote: | Keith: Still confused because I had already found the UR in <36> R79C25 (as per my post). But looking at your grid I still can't see the
UR <23> in R36C79.
Craig |
I ain't Keith, but:
| Code: | +-------------------+-------------------+-------------------+
| 3 2 1 | 7 9 6 | 5 48 48 |
| 78 4 78 | 3 2 5 | 1 6 9 |
| 5 9 6 | 4 1 8 | 23 7 23 |
+-------------------+-------------------+-------------------+
| 489 1 289 | 6 7 3 | 28 5 248 |
| 478 78 3 | 1 5 24 | 6 9 2478 |
| 6 5 27 | 9 8 24 | 237 14 12347 |
+-------------------+-------------------+-------------------+
| 789 3678 5 | 2 36 19 | 4 18 1678 |
| 2 678 789 | 5 4 19 | 78 3 1678 |
| 1 36 4 | 8 36 7 | 9 2 5 |
+-------------------+-------------------+-------------------+
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Note the 23s in r3c79. Also note there is 23 present in r6c79. In r6, 3 is a strong link, so that makes this a Type 4 UR and 2 can be removed from r6c79. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Tue May 20, 2008 6:18 am Post subject: |
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| Quote: | | Note the 23s in r3c79. Also note there is 23 present in r6c79. In r6, 3 is a strong link, so that makes this a Type 4 UR and 2 can be removed from r6c79. |
I believe you can go ahead and call the 3's in row 6 "conjugate" which is why they must remain in r6c79. allowing the elimination of the 2's, breaking up the DP.
just a note on the types of UR's, I have seen them described like this and is what i use to help remember.
type 1 = Unique Corner
type 2 = Unique Side
type 3 = Unique Subset
type 4 = Unique Pair
type 5 = unique diagonal pair
type 6 = unique x-wing??? |
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