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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Fri Aug 14, 2009 4:05 pm Post subject: Free Press 14 August, 2009 |
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This one has me defeated. | Code: | Puzzle: FP081409
+-------+-------+-------+
| 5 . . | 6 . . | . . . |
| 9 . . | 3 . 8 | 5 . . |
| 1 . . | . 4 . | . 8 9 |
+-------+-------+-------+
| 2 . . | . . . | . . . |
| . 6 8 | . . . | 4 2 . |
| . . . | . . . | . . 7 |
+-------+-------+-------+
| 4 2 . | . 1 . | . . 3 |
| . . 1 | 7 . 5 | . . . |
| . . . | . . . | . . 8 |
+-------+-------+-------+ |
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Aug 14, 2009 6:08 pm Post subject: |
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Dang  ___ I can see why Keith encountered problems.
My solver had to be coaxed into reducing it to: chain, chain, XY-Chain.
I hope someone finds something more interesting! |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Fri Aug 14, 2009 11:50 pm Post subject: |
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| Not me, some are too ugly. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Aug 15, 2009 3:30 am Post subject: |
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This LAT puzzle made me come see what had been posted here, so that says something. Here is my solution path:
[1] ALS Chain:
(1=4)r4c4 - ALS[(4)r46c6=(9)r7c6]r3467c6 - (9=3)r5c6 - (3=5)r5c5 - (5=1)r5c9; r5c4|r4c789<>1
This is a nice example of an ALS Chain and shows how useful they can be.
That leads here:
| Code: |
+---------------+---------------+-----------------+
| 5 8 2347 | 6 9 1 | 237 347 24 |
| 9 47 2467 | 3 27 8 | 5 1 246 |
| 1 37 2367 | 5 4 27 | 2367 8 9 |
+---------------+---------------+-----------------+
| 2 149 49 | 14 678 67 | 368 36 5 |
| 7 6 8 | 9 5 3 | 4 2 1 |
| 3 145 45 | 124 268 246 | 689 69 7 |
+---------------+---------------+-----------------+
| 4 2 579 | 8 1 69 | 679 5679 3 |
| 8 39 1 | 7 36 5 | 269 469 246 |
| 6 3579 3579 | 24 23 249 | 1 579 8 |
+---------------+---------------+-----------------+ |
There is now...
[2] 369 XY-Wing: r7c3<>9
[3] Fairly simple AIC:
(2=3)r9c5 - (3)r8c5=(3)r8c2 - (3=7)r3c2 - (7=2)r3c6; r2c5|r9c6<>2
And now...
| Code: |
+---------------+--------------+----------------+
| 5 8 237 | 6 9 1 | 237 347 24 |
| 9 4 26 | 3 7 8 | 5 1 26 |
| 1 37 367 | 5 4 2 | 367 8 9 |
+---------------+--------------+----------------+
| 2 19 49 | 14 68 7 | 368 36 5 |
| 7 6 8 | 9 5 3 | 4 2 1 |
| 3 15 45 | 124 268 46 | 689 69 7 |
+---------------+--------------+----------------+
| 4 2 57 | 8 1 69 | 679 5679 3 |
| 8 39 1 | 7 36 5 | 269 469 246 |
| 6 3579 3579 | 24 23 49 | 1 579 8 |
+---------------+--------------+----------------+ |
There is a not very useful 469 XY-Wing which I ignore. Instead...
[4] M-Wing:
(4=9)r9c6 - (9)r9c3=(9-4)r4c3=(4)r4c4; r6c6|r9c4<>4
This solves the puzzle. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Aug 15, 2009 5:01 am Post subject: |
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| Code: | .---------------------.---------------------.---------------------.
| 5 8 2347 | 6 9 1 | 237 347 24 |
| 9 47 2467 | 3 27 8 | 5 1467 1246 |
| 1 37 2367 | 5 4 27 | 2367 8 9 |
:---------------------+---------------------+---------------------:
| 2 1459 459 | 14 5678 467 | 13689 1369 156 |
| 7 6 8 | 19 35 39 | 4 2 15 |
| 3 1459 459 | 124 2568 246 | 1689 169 7 |
:---------------------+---------------------+---------------------:
| 4 2 579 | 8 1 69 | 679 5679 3 |
| 8 39 1 | 7 236 5 | 269 469 246 |
| 6 3579 3579 | 249 23 2349 | 1279 1579 8 |
'---------------------'---------------------'---------------------' |
1...(23)r89c5 = (6)r8c5 - (6=9)r7c6 - (9=3)r5c6; r5c5 <> 3
2...(7=6)r4c6 - (6)r7c6 = (6-3)r8c5 = (3)r8c2 - (3=7)r3c2; r3c6 <> 7
3...(3=9)r8c2 - (9=1)r4c2 - (1=4)r4c4 - (4=2)r9c4 - (2=3)r9c5; r9c23 <> 3 |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Aug 15, 2009 7:21 am Post subject: |
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Chains? In that case, after basics: | Code: | +-------------------+-------------------+-------------------+
| 5 8 2347 | 6 9 1 | 237 347 24 |
| 9 4-7 246-7 | 3 27e 8 | 5 1467 1246 |
| 1 37a 2367 | 5 4 2-7 | 2367 8 9 |
+-------------------+-------------------+-------------------+
| 2 1459 459 | 14 5678 467 | 13689 1369 156 |
| 7 6 8 | 19 35 39 | 4 2 15 |
| 3 1459 459 | 124 2568 246 | 1689 169 7 |
+-------------------+-------------------+-------------------+
| 4 2 579 | 8 1 69 | 679 5679 3 |
| 8 39b 1 | 7 236c 5 | 269 469 246 |
| 6 3579 3579 | 249 23d 2349 | 1279 1579 8 |
+-------------------+-------------------+-------------------+ |
If a is 3, b is 9, c is 3, d is 2, e is 7. ae are pincers on 7. Leading to a 4-cell chain (XY-wing with pseudocell): | Code: | +-------------------+-------------------+-------------------+
| 5 8 237 | 6 9 1 | 237 347 24 |
| 9 4 26 | 3 7 8 | 5 16 126 |
| 1 37 367 | 5 4 2 | 367 8 9 |
+-------------------+-------------------+-------------------+
| 2 159 459 | 14b 568 7 | 13689 1369 156 |
| 7 6 8 | 19a 35 3-9 | 4 2 15 |
| 3 159 459 | 124 2568 46c | 1689 169 7 |
+-------------------+-------------------+-------------------+
| 4 2 579 | 8 1 69d | 679 5679 3 |
| 8 39 1 | 7 236 5 | 269 469 246 |
| 6 3579 3579 |24-9 23 349 | 1279 1579 8 |
+-------------------+-------------------+-------------------+ |
Now there are two XY-wings, abc and def: | Code: | +----------------+----------------+----------------+
| 5 8 237 | 6 9 1 | 237 347 24 |
| 9 4 26 | 3 7 8 | 5 1 26 |
| 1 37 367 | 5 4 2 | 367 8 9 |
+----------------+----------------+----------------+
| 2 19 49 | 14 68 7 | 368 36 5 |
| 7 6 8 | 9 5 3 | 4 2 1 |
| 3 15 45 | 124 268 46b | 689 69c 7 |
+----------------+----------------+----------------+
| 4 2 57-9 | 8 1 69f | 679 5679 3 |
| 8 39d 1 | 7 36e 5 | 269 469 246 |
| 6 3579 3579 | 24 23 49a | 1 57-9 8 |
+----------------+----------------+----------------+ |
This reveals an half-M-wing on 49: | Code: | +----------------+----------------+----------------+
| 5 8 237 | 6 9 1 | 237 347 24 |
| 9 4 26 | 3 7 8 | 5 1 26 |
| 1 37 367 | 5 4 2 | 367 8 9 |
+----------------+----------------+----------------+
| 2 19 49# | 14@ 68 7 | 368 36 5 |
| 7 6 8 | 9 5 3 | 4 2 1 |
| 3 15 45 | 124 268 -46 | 689 69 7 |
+----------------+----------------+----------------+
| 4 2 57 | 8 1 69 | 679 5679 3 |
| 8 39 1 | 7 36 5 | 269 469 246 |
| 6 3579* 3579*|2-4 23 49@ | 1 57 8 |
+----------------+----------------+----------------+ |
The cells @ are pincers on 4, solving the puzzle.
Keith |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Aug 15, 2009 8:59 am Post subject: |
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Norm,
Your first step can be viewed as a classic two-ALS technique, with shared common <3> and shared exclusive/restricted common <6>. So, it can escape the "chain" "approbation"! This view is best conveyed in Eureka thus:
ALS[(3)r89c5=(6)r8c5] - ALS[(6)r7c6=(3)r5c6]; r5c3|r9c6<>3
The two ALS technique is, of course, just a very short ALS Chain! (And, XY- and XYZ-Wings are just special cases of the more general two ALS technique.)
Interestingly, it leads to the same grid as my first step did. Still, I don't believe there is any escaping the use of chains in solving this puzzle... not that there's anything wrong with that. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat Aug 15, 2009 1:15 pm Post subject: |
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Since everyone is going with chains ...
After basics, a nice combination of strong links on <3>, <4>, and <9>.
| Code: | ( 3)r5c6 = (3-4)r9c6 = (4-9)r9c4 = (9)r5c4 => [r5c6]<>9
(9-3)r5c6 = (3-4)r9c6 = (4-9)r9c4 = (9)r5c4 - (9)r5c6 => [r5c6]<>9
+-----------------------------------------------------------------------+
| 5 8 2347 | 6 9 1 | 237 347 24 |
| 9 47 2467 | 3 27 8 | 5 1467 1246 |
| 1 37 2367 | 5 4 27 | 2367 8 9 |
|-----------------------+-----------------------+-----------------------|
| 2 1459 459 | 14 5678 467 | 13689 1369 156 |
| 7 6 8 | 19 35 3-9 | 4 2 15 |
| 3 1459 459 | 124 2568 246 | 1689 169 7 |
|-----------------------+-----------------------+-----------------------|
| 4 2 579 | 8 1 69 | 679 5679 3 |
| 8 39 1 | 7 236 5 | 269 469 246 |
| 6 3579 3579 | 249 23 2349 | 1279 1579 8 |
+-----------------------------------------------------------------------+
# 103 eliminations remain
|
Extraneous <36+9> XY-Wing.
| Code: | ( 7)r4c6 = r3c6 - (7=3)r3c2 - r8c2 = (3-6)r8c5 = (6)r7c6 => [r4c6]<>6
(6-7)r4c6 = r3c6 - (7=3)r3c2 - r8c2 = (3-6)r8c5 = (6)r7c6 - (6)r4c6 => [r4c6]<>6
+--------------------------------------------------------------+
| 5 8 2347 | 6 9 1 | 237 347 24 |
| 9 47 2467 | 3 27 8 | 5 1 246 |
| 1 37 2367 | 5 4 27 | 2367 8 9 |
|--------------------+--------------------+--------------------|
| 2 149 49 | 14 678 7-6 | 368 36 5 |
| 7 6 8 | 9 5 3 | 4 2 1 |
| 3 145 45 | 124 268 246 | 689 69 7 |
|--------------------+--------------------+--------------------|
| 4 2 579 | 8 1 69 | 679 5679 3 |
| 8 39 1 | 7 36 5 | 269 469 246 |
| 6 3579 3579 | 24 23 249 | 1 579 8 |
+--------------------------------------------------------------+
# 73 eliminations remain
|
Extraneous <46+9> XY-Wing. The (half) M-Wing is a better choice than my XY-Chain.
| Code: | (3=9)r8c2 - (9=1)r4c2 - (1=4)r4c4 - (4=2)r9c4 - (2=3)r9c5 => [r8c5],[r9c23]<>3
+--------------------------------------------------------------+
| 5 8 237 | 6 9 1 | 237 347 24 |
| 9 4 26 | 3 7 8 | 5 1 26 |
| 1 37 367 | 5 4 2 | 367 8 9 |
|--------------------+--------------------+--------------------|
| 2 19 49 | 14 68 7 | 368 36 5 |
| 7 6 8 | 9 5 3 | 4 2 1 |
| 3 15 45 | 124 268 46 | 689 69 7 |
|--------------------+--------------------+--------------------|
| 4 2 57 | 8 1 69 | 679 5679 3 |
| 8 39 1 | 7 6-3 5 | 269 469 246 |
| 6 579-3 579-3 | 24 23 49 | 1 579 8 |
+--------------------------------------------------------------+
# 57 eliminations remain
|
===== ===== ===== Also
Normally, I don't follow ALS chains. But Asellus' first ALS chain caught my attention, and so I investigated the ALS cells.
This PM presents an interesting observation.
If [r4c6]=7 and [r6c6]=2, then bivalue cell [r3c6] is forced empty. Therefore, one of [r46c6] must be <4> or <6>.
{ ???: (4=6)r46c6 }
| Code: | (9=1)r5c4 - (1=4)r4c4 - ???[(4=6)r46c6] - (6=9)r7c6 => [r5c6],[r9c4]<>9
+-----------------------------------------------------------------------+
| 5 8 2347 | 6 9 1 | 237 347 24 |
| 9 47 2467 | 3 27 8 | 5 1467 1246 |
| 1 37 2367 | 5 4 27 | 2367 8 9 |
|-----------------------+-----------------------+-----------------------|
| 2 1459 459 | 14 5678 46+7 | 13689 1369 156 |
| 7 6 8 | 19 35 3-9 | 4 2 15 |
| 3 1459 459 | 124 2568 46+2 | 1689 169 7 |
|-----------------------+-----------------------+-----------------------|
| 4 2 579 | 8 1 69 | 679 5679 3 |
| 8 39 1 | 7 236 5 | 269 469 246 |
| 6 3579 3579 | 24-9 23 2349 | 1279 1579 8 |
+-----------------------------------------------------------------------+
# 103 eliminations remain
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Aug 15, 2009 11:44 pm Post subject: |
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| daj95376 wrote: | This PM presents an interesting observation.
If [r4c6]=7 and [r6c6]=2, then bivalue cell [r3c6] is forced empty. Therefore, one of [r46c6] must be <4> or <6>.
{ ???: (4=6)r46c6 } |
Yes, all ALS work this way. The thing to realize about ALS is that any (grouped) candidate within an ALS has a strong inference with any other (grouped) candidate in that ALS.
In this case, you are using the 2467 ALS in r346c6 and exploiting the strong inference:
ALS[(4)r46c6=(6)r46c6]r346c6
The notation can be abbreviated as you have done though I recommend including the ALS reference so that the source of the inference is explicit:
ALS[(4=6)r46c6]r346c6
It is not necessary to think about the forcings ("if <2> and <7> then goodbye bivalue"). One only needs to recognize that every ALS contains such strong inferences. There are as many strong inferences inherent in an ALS as there are combinations of the grouped digits, though many of these inferences are often of no use. Here are the inferences inherent in this 2467 ALS:
(2)r36c6=(4)r46c6
(2)r36c6=(6)r46c6
(2)r36c6=(7)r34c6
(4)r46c6=(6)r46c6
(4)r46c6=(7)r34c6
(6)r46c6=(7)r34c6
I know that all of these strong inferences exist without any "if-then" thinking. It should be obvious that all instances of any two candidates within an ALS cannot both be false (since some cell will be left with no candidate). That is the definition of a strong inference. The strong inference within a bivalue cell is the simplest case of strong inference inherent in an ALS. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sun Aug 16, 2009 12:11 am Post subject: |
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Thanks Asellus!!! I'll give what you said some closer review.
===== ===== ===== Later
So, it appears that I was using a shorter ALS in a chain segment to do the same thing as your ALS.
| Code: | Asellus ALS: ALS[(4)r46c6=(9)r7c6]r3467c6
DAJ Bumbling: ALS[(4=6)r46c6]r346c6 - (6=9)r7c6
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Tue Aug 18, 2009 7:30 am Post subject: |
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| Keith wrote: | | Leading to a 4-cell chain (XY-wing with pseudocell): |
| Code: | +-------------------+-------------------+-------------------+
| 5 8 237 | 6 9 1 | 237 347 24 |
| 9 4 26 | 3 7 8 | 5 16 126 |
| 1 37 367 | 5 4 2 | 367 8 9 |
+-------------------+-------------------+-------------------+
| 2 159 459 |*14 568 7 | 13689 1369 156 |
| 7 6 8 |*19 35 3-9 | 4 2 15 |
| 3 159 459 |*124 2568 *46 | 1689 169 7 |
+-------------------+-------------------+-------------------+
| 4 2 579 | 8 1 69 | 679 5679 3 |
| 8 39 1 | 7 236 5 | 269 469 246 |
| 6 3579 3579 |24-9 23 349 | 1279 1579 8 |
+-------------------+-------------------+-------------------+ |
Configurations like this get my attention as particularly ripe ALSs. It has three candidates (269) that do not repeat within the set, which extends the potential reach of the ALS. Possibilities abound:
| Code: | (1469=2)
(1249=6)
(1246=9)
Heck, even:
(2469=group 1s) |
This one pays off with the elims you cited, short'n'sweet: | Code: | | (9=6)r7c6-(6=1249)r6c6,r456c4. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue Aug 18, 2009 11:46 am Post subject: |
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| daj95376 wrote: | | DAJ Bumbling |
Not at all! I just happened to see it as a 4-cell ALS. You saw it as a 3-cell ALS + 1-cell ALS. Nothing wrong with that. I could just as easily have happened to see it that way myself. It is valid in any case. (My point had to do with seeing inferences rather than forcings.)
Luke451, I like your two ALS step. But, I would notate it differently:
(9=6)r7c6 - ALS[(6)r6c6=(9)r5c4]r456c4|r6c6; r5c6|r9c4<>9
However, you could also drop the cell with the <2> and just use the 3-cell 1469 ALS:
(9=6)r7c6 - ALS[(6)r6c6=(9)r5c4]r45c4|r6c6; r5c6|r9c4<>9
But this is just collapsing Keith's 3 1-cell bivalue ALS chain segment into a single 3-cell ALS. Because (6=4)r6c6 and (4=1)r4c4 and (1=9)r5c4 are all peers in b5, they can be collapsed into the 3-cell ALS. It's the same situation as me and daj. You say poTAYto, I say poTAHto. Either way, it tastes good. I can't see that the flavor is improved in any way by saying that it is a 2 ALS technique instead of a 4-cell XY Chain, or vice-versa.
I'm with you about AICs. Ultimately, almost everything in sudoku boils down to AICs. Larger patterns start to emerge which are not confined to named techniques. The named techniques become special cases and limited applications of more general principles. All that remains is to make the roads clear enough for those who are willing to follow after and find their way to those more general principles. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed Aug 19, 2009 9:47 am Post subject: |
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I have a question.
alright, so lets say you take my first step above...r5c5 and r9c6 <> 3
then some singles.
followed by a xy-wing {3,6,9} removes 9 from r7c3
you get to this grid.
notice the 5's and 7's in the third band that I have marked in this grid.
| Code: | +---------------+---------------+--------------------+
| 5 8 2347 | 6 9 1 | 237 347 24 |
| 9 47 2467 | 3 27 8 | 5 1 246 |
| 1 37 2367 | 5 4 27 | 2367 8 9 |
+---------------+---------------+--------------------+
| 2 149 49 | 14 678 67 | 368 36 5 |
| 7 6 8 | 9 5 3 | 4 2 1 |
| 3 145 45 | 124 268 246 | 689 69 7 |
+---------------+---------------+--------------------+
| 4 2 (57) | 8 1 69 | 69(7) 69(57) 3 |
| 8 39 1 | 7 36 5 | 269 469 246 |
| 6 3579 3579 | 24 23 249 | 1 -9(57) 8 |
+---------------+---------------+--------------------+
|
I can see this as a continous loop.
(5)r9c8 = (5)r7c8 - (5=7)r7c3 - (7)r7c78 = (7)r9c8; r9c8 <> 9
I may have seen this type of loop twice before.
I know that sudecoq can sometimes be expressed as a continous loop.
Is this loop part of a sudecoq that I can't see or maybe another ALS/subset counting move? |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Wed Aug 19, 2009 5:04 pm Post subject: |
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Sup, Norm. I think you're onto something.
| Code: | *-----------------------------------------------------------*
| 5 8 2347 | 6 9 1 | 237 347 24 |
| 9 47 2467 | 3 27 8 | 5 1 246 |
| 1 37 2367 | 5 4 27 | 2367 8 9 |
|-------------------+-------------------+-------------------|
| 2 149 49 | 14 678 67 | 368 36 5 |
| 7 6 8 | 9 5 3 | 4 2 1 |
| 3 145 45 | 124 268 246 | 689 69 7 |
|-------------------+-------------------+-------------------|
| 4 2 *57 | 8 1 69 |*679 *5679 3 |
| 8 39 1 | 7 36 5 |*269 *469 *246 |
| 6 3579 3579 | 24 23 249 | 1 57-9 8 |
*-----------------------------------------------------------* |
That's six cells, six candidates (245679), with a disjoint node. That's an SdC in my book.
Interestingly enuf, there's a sympathetic one below:
| Code: | *-----------------------------------------------------------*
| 5 8 2347 | 6 9 1 | 237 347 24 |
| 9 47 2467 | 3 27 8 | 5 1 246 |
| 1 37 2367 | 5 4 27 | 2367 8 9 |
|-------------------+-------------------+-------------------|
| 2 149 49 | 14 678 67 | 368 36 5 |
| 7 6 8 | 9 5 3 | 4 2 1 |
| 3 145 45 | 124 268 246 | 689 69 7 |
|-------------------+-------------------+-------------------|
| 4 2 *57 | 8 1 69 | 679 5679 3 |
| 8 39 1 | 7 36 5 | 269 469 246 |
| 6 *3579 *3579 |*24 *23 *249 | 1 57-9 8 |
*-----------------------------------------------------------* |
Once again, six cells, six candidates, (234579), etc. Same elim.
As Asellus was saying, behind almost every pattern with a name there lies a chain. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed Aug 19, 2009 7:27 pm Post subject: |
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Hi luke,
so there is a sudecoq present when combining other candidates, I would never have found that as I don't search for them.
does the condition have a name when only looking at the 5's and 7's as a loop?
Does this not look like a m-wing loop?
wasn't there an example of a M-wing loop previously in the forum? if so I bet it was posted by nataraj.
| Code: | M-wing: (A=B) - B = (B-A) = A
| |
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|-pincers when in different houses
example: (7=5) - 5 = (5-7) = 7
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|-loop when in same house |
i am going to change the M-wing a little so that it doesn't overlap and hopefully is clearer to see.
to...(7=5)r7c3 - (5)r7c8 = (5-7)r9c8 = (7)r9c23
I am pretty sure this was brought up before but I can't remember seeing it in a while in this forum.
Last edited by storm_norm on Wed Aug 19, 2009 11:03 pm; edited 1 time in total |
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Luke451
Joined: 20 Apr 2008
Posts: 310
Location: Southern Northern California
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| Posted: Wed Aug 19, 2009 8:40 pm Post subject: |
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Yeah, that does follow the M-wing pattern exactly  .
I'm not sure why you wouldn't write it like this, though:
(7=5)r7c3 - (5)r7c8 = (5-7)r9c8 = (7)r9c23 -etc, and the same hapless 9 is eliminated with all links conjugate.
(In fact, it don't matter what you throw at 9r9c8, it'll stick.
ALS-xz
(23469)r8c5789
(2349)r9c456
RC=3
OC=9) |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Wed Aug 19, 2009 11:03 pm Post subject: |
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| Quote: | | (7=5)r7c3 - (5)r7c8 = (5-7)r9c8 = (7)r9c23 -etc, and the same hapless 9 is eliminated with all links conjugate |
oops, I meant it the way you wrote it. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Aug 20, 2009 12:29 am Post subject: |
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As I recall,
The M-wing loop was noticed by re'born. If the pincers are in the same house, you have a loop where each link makes an elimination in the variable that the end cells of the link share.
http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2143
I think the same applies to a W-wing.
I believe the same applies to any "closed" XY-chain.
Keith |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Aug 20, 2009 1:44 am Post subject: |
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| keith wrote: | As I recall,
The M-wing loop was noticed by re'born. If the pincers are in the same house, you have a loop where each link makes an elimination in the variable that the end cells of the link share.
http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=2143
I think the same applies to a W-wing.
I believe the same applies to any "closed" XY-chain.
Keith |
aha.
thank you. |
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strmckr
Joined: 18 Aug 2009
Posts: 66
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| Posted: Thu Aug 20, 2009 7:08 am Post subject: |
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after ss:
start with
vwxyz wing(als-xz): A=r7c6 {69}, B=r456c4,r6c6 {12469}, X=6, Z=9 => r5c6,r9c4<>9
or
wxyz wing: A=r5c6 {39}, B=r7c6,r89c5 {2369}, X=9, Z=3 => r5c5,r9c6<>3
more ss:
Death Blossom: [r9c5], -2- r2c25 {247}, -3- r4679c3 {34579} => r12c3,r46c2<>4, r2c3<>7
more ss:
Death Blossom: [r4c4], -1- r48c2 {139}, -4- r9c45 {234} => r8c5,r9c23<>3
ss to the end... |
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