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| noeldillabough
| | Joined: 12 Oct 2005 | | Posts: 16 | | : | |
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 Posted: Sun Oct 30, 2005 12:58 am Post subject: Misunderstanding XYZ-WIng pattern |
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It seems I misunderstand the XYZ-Wing pattern; I get to here and my thought was that there is a valid XYZ-Wing as follows:
| Code: |
731|469|5..
698|2.5|.47
524|..7|9.6
---+---+---
3.9|.5.|.7.
1..|9.2|.5.
25.|.4.|8.9
---+---+---
872|59.|4.1
913|..4|..5
465|1..|79.
731469500698205047524007906309050070100902050250040809872590401913004005465100790
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XYZWing at (3,8) <-- (6,8) --> (5,7) removes 3 at (2,7)
However i know from the solution this is incorrect as there is a 3 at (2,7).
r3c8 needs {1 3}
r6c8 needs {1 3 6}
r5c7 needs {3 6}
So I *think* this is a valid XYZ-Wing, however I tried it in Susser and it says that's not a valid XYZ-Wing pattern.
What am I misunderstanding?
-Noel |
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| noeldillabough
| | Joined: 12 Oct 2005 | | Posts: 16 | | : | |
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| Posted: Sun Oct 30, 2005 1:05 am Post subject: NVM |
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Just reading Robert's (fantastic) manual for Susser and sure enough the answer's there...
Squares that are buddies with *all three of the squares* cannot contain Z. |
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| rkral
| | Joined: 21 Oct 2005 | | Posts: 233 | | : | |
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| Posted: Sun Oct 30, 2005 1:35 pm Post subject: Re: Misunderstanding XYZ-WIng pattern |
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[edit: I see you figured it out, but I'll let this message stand anyway.]
| noeldillabough wrote: | So I *think* this is a valid XYZ-Wing, however I tried it in Susser and it says that's not a valid XYZ-Wing pattern.
What am I misunderstanding? |
It looks like a valid XYZ-wing pattern to me, but the possible eliminations of Z would be at r4c8 and r5c8. Those are the cells at the intersect of col 8 and box 6, and excluding r6c8 which is part of the XYZ.
See http://www.setbb.com/phpbb/viewtopic.php?t=252&highlight=&mforum=sudoku |
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| Bob Hanson
| | Joined: 05 Oct 2005 | | Posts: 187 | | : | | Location: St. Olaf College |
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| Posted: Thu Nov 03, 2005 5:58 am Post subject: |
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As Noel relates, it isn't a valid xyz-wing.
see http://www.stolaf.edu/people/hansonr/sudoku/explain.htm for why.
Sudoku Assistant reports the next step to be:
r6c8 ISN'T 6: strong incompatibility on 6 at cell r6c8 (involving nodes r6c3#6 chain 2(1) and r6c8#1 chain 2(0))
It's a rather involved chain:
| Code: |
5 r2c5#1 chain 2(1)
6 r2c7#1 chain 2(0)
7 r3c5#1 chain 2(0)
8 r2c5#3 chain 2(0)
9 r2c7#3 chain 2(1)
16 r3c8#1 chain 2(1)
17 r3c8#3 chain 2(0)
19 r5c3#6 chain 2(0)
20 r6c3#6 chain 2(1)
21 r5c3#7 chain 2(1)
22 r6c3#7 chain 2(0)
23 r4c6#1 chain 2(0)
24 r4c7#1 chain 2(1)
31 r6c4#7 chain 2(1)
32 r8c4#7 chain 2(0)
33 r6c6#1 chain 2(1)
37 r5c7#6 chain 2(1)
38 r5c5#7 chain 2(0)
39 r8c5#7 chain 2(1)
40 r5c7#3 chain 2(0)
43 r6c8#1 chain 2(0)
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But it does do the job. After that, the puzzle is trivial.
_________________
Bob Hanson
Professor of Chemistry
St. Olaf College
Northfield, MN
http://www.stolaf.edu/people/hansonr |
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| rkral
| | Joined: 21 Oct 2005 | | Posts: 233 | | : | |
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| Posted: Thu Nov 03, 2005 11:13 am Post subject: |
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| Bob Hanson wrote: | | As Noel relates, it isn't a valid xyz-wing. |
Depends upon what one means by "valid". If you mean that identifying this particular xyz-wing doesn't lead to reduction of the puzzle, I agree.
But r3c8=13, r5c7=36, and r6c8=136 is indeed an xyz-wing pattern. It's just that no reduction is possible because r4c8 and r5c8 are already filled or pinned.
| Code: |
*--------------------------------------------------*
| 7 3 1 | 4 6 9 | 5 28 28 |
| 6 9 8 | 2 13 5 | 13 4 7 |
| 5 2 4 | 38 138 7 | 9 13 6 |
|----------------+----------------+----------------|
| 3 48 9 | 68 5 168 | 126 7 24 |
| 1 48 67 | 9 378 2 | 36 5 34 |
| 2 5 67 | 367 4 136 | 8 136 9 |
|----------------+----------------+----------------|
| 8 7 2 | 5 9 36 | 4 36 1 |
| 9 1 3 | 678 278 4 | 26 268 5 |
| 4 6 5 | 1 238 38 | 7 9 238 |
*--------------------------------------------------*
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| Ruud
Site Admin
 | | Joined: 17 Sep 2005 | | Posts: 708 | | : | | Location: Netherlands |
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| Posted: Thu Nov 03, 2005 7:59 pm Post subject: |
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| rkral wrote: | | Depends upon what one means by "valid". |
It also depends on the definition, whether ot not it includes the "victims".
For example: A naked subset is still a naked subset after you eliminate the victims, but a hidden subset ceases to exist when you're done with it.
The proper term to use here would be "effective", not "valid", I guess...
Ruud. |
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| xyzzy
| | Joined: 24 Aug 2005 | | Posts: 80 | | : | |
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| Posted: Thu Nov 03, 2005 8:05 pm Post subject: |
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| Ruud wrote: |
For example: A naked subset is still a naked subset after you eliminate the victims, but a hidden subset ceases to exist when you're done with it.
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How do you figure that? The naked subset disappearing. |
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| Bob Hanson
| | Joined: 05 Oct 2005 | | Posts: 187 | | : | | Location: St. Olaf College |
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| Posted: Sun Nov 06, 2005 8:27 pm Post subject: |
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Well, I agree with Ruud, in the sense that it IS, sort of, an xyz-wing.
What we were saying was that it can't delete the 3 at r2c7.
It's stronger than a standard xyz-wing, though. With a standard xyz-wing we have:
| Code: |
c7 c8 c9
r3 | 9 13 6 |
ss
+----------------|
r4 | 126 7 24 |
r5 | 36 5 34 |
ss
r6 | 8 136 9 |
wcw
s=strong node; w=weak node; l=weak link; c=weak corner
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But here we have (because there are no other 1s in column 8):
| Code: |
c7 c8 c9
r3 | 9 13 6 |
ss
+----------------|
r4 | 126 7 24 |
r5 | 36 5 34 |
ss
r6 | 8 136 9 |
scc
s=strong node; w=weak node; l=weak link; c=weak corner
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(Lot's more in there, I'm just not indicating them.)
I don't think it makes that much difference in this case, though.
No "3" is in the "path" of both the XZ and the YZ (r4c8 and r5c8 in this case)
_________________
Bob Hanson
Professor of Chemistry
St. Olaf College
Northfield, MN
http://www.stolaf.edu/people/hansonr |
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| rubylips
| | Joined: 07 Apr 2005 | | Posts: 62 | | : | | Location: London |
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| Posted: Sun Nov 06, 2005 9:27 pm Post subject: |
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I'm not sure whether the point of this thread is to solve the puzzle or to discuss the definition of XYZ-Wing but here's a reasonably straightforward solution:
| Code: | The values 2 and 8 occupy the cells r1c8 and r8c8 in some order.
- The move r8c8:=6 has been eliminated.
Consider the chain r6c4~6~r6c8-6-r7c8-6-r7c6-6-r8c4.
When the cell r6c4 contains the value 6, so does the cell r8c4 - a contradiction.
Therefore, the cell r6c4 cannot contain the value 6.
- The move r6c4:=6 has been eliminated.
Consider the chain r3c5-8-r3c4-3-r6c4-7-r5c5.
When the cell r5c5 contains the value 8, some other value must occupy the cell r3c5, which means that the value 7 must occupy the cell r5c5 - a contradiction.
Therefore, the cell r5c5 cannot contain the value 8.
- The move r5c5:=8 has been eliminated.
The cell r5c2 is the only candidate for the value 8 in Row 5.
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The chain in 8, 3 and 7 is the critical step. The text that precedes it isn't a logical prerequisite.
_________________
Java 5.0 Solver/Composer Applet: http://act365.com/sudoku
GPL Source Code: http://sf.net/projects/sudoku |
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