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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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 Posted: Wed Dec 14, 2011 8:51 am Post subject: rh121411 |
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| Code: | *-----------*
|..7|...|...|
|.49|.26|...|
|81.|34.|..2|
|---+---+---|
|29.|87.|...|
|...|...|...|
|...|.92|.85|
|---+---+---|
|9..|.35|.27|
|...|98.|45.|
|...|...|9..|
*-----------*
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Wed Dec 14, 2011 3:57 pm Post subject: |
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After basics:
| Code: | *-----------------------------------------------------------*
| 3 2 7 | 15 15 8 | 6 49 49 |
| 5 4 9 | 7 2 6 | 138 13 138 |
| 8 1 6 | 3 4 9 | 5 7 2 |
|-------------------+-------------------+-------------------|
| 2 9 5 | 8 7 134 | 13 1346 1346 |
| 1467 678 148 | 1456 156 134 | 2 1349 1349 |
| 146 36 134 | 146 9 2 | 7 8 5 |
|-------------------+-------------------+-------------------|
| 9 68 148 | 146 3 5 | 18 2 7 |
| 167 367 2 | 9 8 17 | 4 5 136 |
| 1467 5 1348 | 2 16 147 | 9 136 1368 |
*-----------------------------------------------------------* |
Short chain....
(7=1)r8c6-(1=6)r9c5-r9c89=(6-3)r8c9=r8c2; r8c2<>7
Ted |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Wed Dec 14, 2011 9:20 pm Post subject: |
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| Code: | *-----------------------------------------------------------*
| 3 2 7 | 15 15 8 | 6 49 49 |
| 5 4 9 | 7 2 6 | 138 13 138 |
| 8 1 6 | 3 4 9 | 5 7 2 |
|-------------------+-------------------+-------------------|
| 2 9 5 | 8 7 134 | 13 1346 1346 |
| 1467 678 148 | 1456 156 134 | 2 1349 1349 |
| 146 a36 134 | 146 9 2 | 7 8 5 |
|-------------------+-------------------+-------------------|
| 9 8-6 148 | 146 3 5 | 18 2 7 |
|d167 bd367 2 | 9 8 17 | 4 5 c136 |
| 1467 5 1348 | 2 16 147 | 9 136 1368 |
*-----------------------------------------------------------*
m-wing
(6=3)r6c2-(3)r8c2=(3-6)r8c9..=(6)r8c12 => r7c2<>6
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Wed Dec 14, 2011 10:02 pm Post subject: |
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Another POV ... 
ALS-XZ : (6=3)r3c2-(3=167)r8c126 => -6r7c2 |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Dec 15, 2011 12:06 am Post subject: |
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| JC Van Hay wrote: | Another POV ...
ALS-XZ : (6=3)r6c2-(3=167)r8c126 => -6r7c2 |
My solver found a variant of JC's ALS-XZ.
| Code: | (6=17)r8c16 - (7=36)r68c2 => r7c2<>6
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What caught my attention was the 3x URs that (seemingly) did nothing to advance an alternate solution.
| Code: | +-----------------------------------------------------------------+
| 3 2 7 | *15 *15 8 | 6 *49 *49 |
| 5 4 9 | 7 2 6 | 138 13 138 |
| 8 1 6 | 3 4 9 | 5 7 2 |
|---------------------+---------------------+---------------------|
| 2 9 5 | 8 7 134 | %13 46-13 46-13 |
| *67+14 *67+8 148 | *15+46 *15+6 134 | 2 *49+13 *49+13 |
| 146 36 134 | 146 9 2 | 7 8 5 |
|---------------------+---------------------+---------------------|
| 9 68 148 | 146 3 5 | 18 2 7 |
| *67+1 *67+3 2 | 9 8 %17 | 4 5 136 |
| 1467 5 1348 | 2 16 147 | 9 136 1368 |
+-----------------------------------------------------------------+
# 72 eliminations remain
r15c89 <49> UR Type 3.2244 <> 13 r4c89 ( using r4c7 )
r15c45 <15> UR Type 4.2243 <> 1 r5c45
r58c12 <67> UR via s-link + N_Singles <> 6 r5c2 ( using r8c6 )
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Dec 15, 2011 12:49 am Post subject: |
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ER (4); r5c3<>4
W-Wing (18), SL 8 in c9; r7c3<>1 + transport; r7c4<>1
Type 2 UR (49-1); numerous eliminations |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Thu Dec 15, 2011 3:42 am Post subject: |
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| daj95376 wrote: | | JC Van Hay wrote: | Another POV ...
ALS-XZ : (6=3)r6c2-(3=167)r8c126 => -6r7c2 |
My solver found a variant of JC's ALS-XZ.
| Code: | (6=17)r8c16 - (7=36)r68c2 => r7c2<>6
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Danny, I call your solution an "almost naked pair".
Ted |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Thu Dec 15, 2011 4:32 am Post subject: |
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| tlanglet wrote: | | daj95376 wrote: | My solver found a variant of JC's ALS-XZ.
| Code: | (6=17)r8c16 - (7=36)r68c2 => r7c2<>6
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I call your solution an "almost naked pair". |
Yes, if it helps to think of it that way, every als-xz is comprised of two "almost naked sets."  |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Dec 15, 2011 4:43 am Post subject: |
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| tlanglet wrote: | Danny, I call your solution an "almost naked pair".
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I can understand you calling it that. Each strong inference is comprised of an almost naked pair.
When I checked the definitions at Sudopedia, the description for an ALS XY-Chain seemed to match my "chain". There may be a hangup, though, in the weak inference not having identical values on each side.
That description also included this statement:
| Sudokedia wrote: | The ALS-XZ rule is an ALS-XY-Chain of length two, while the ALS-XY-Wing is an ALS-XY-Chain of length three.
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If my chain does qualify as an ALS XY-Chain, then it also qualifies as an ALS-XZ.
Regards, Danny
Note: I noticed that ronk had included a reply while I was composing this message. I'm posting it anyway ... just in case some aspect is incorrect. |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Thu Dec 15, 2011 11:49 am Post subject: |
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| daj95376 wrote: | | There may be a hangup, though, in the weak inference not having identical values on each side. |
If by "on each side" you mean this AIC expression ... (6=17)r8c16 - (7=36)r68c2 => r7c2<>6 ... IMO it would be improved if written as ...
(16=7)r8c16 - (7=36)r68c2 ... or maybe even ... (61=7)r8c16 - (7=36)r68c2
IOW there should be left-right symmetry in the AIC for two almost-naked-pairs. |
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JC Van Hay
Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium
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| Posted: Thu Dec 15, 2011 1:18 pm Post subject: |
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| daj95376 wrote: | | Code: | (6=17)r8c16 - (7=36)r68c2 => r7c2<>6
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Still another POV, but not so trivial in more complex cases, ...
AHP(6r8c1=36r8c29)-AHP(7r8c2=78r58c2) => -6r7c2 |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Thu Dec 15, 2011 1:49 pm Post subject: |
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| arkietech wrote: | m-wing
(6=3)r6c2-(3)r8c2=(3-6)r8c9=(6)r8c12 => r7c2<>6 |
I like this the best and, with only three native strong inferences, it's probably unbeatable as a one-step solution. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Dec 15, 2011 10:59 pm Post subject: |
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| ronk wrote: | ... or maybe even ... (61=7)r8c16 - (7=36)r68c2
IOW there should be left-right symmetry in the AIC for two almost-naked-pairs. |
Hmmm. Interesting! After my comment, I started looking for another way to write the left strong inference term, but I couldn't convince myself to accept it as you indicated because it doesn't work as an ANP(). Now, with a fresh look, I see how it works just fine as an ALS(network). Thanks!!!
Unfortunately, my solver doesn't create your ALS as a strong inference. _  _
JC, an interesting use of the AHP(). I've been considering adding an almost Hidden Subset, AHS(), module to my solver, but it's creating so many SIs now that the execution time has increased drastically. I'm afraid of what will happen to the execution time if I add any more SIs. _  _
Regards, Danny |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Fri Dec 16, 2011 11:46 pm Post subject: |
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Just to satisfy my curiosity... Why would someone consider it fine to notate a locked set object on one end of a strong inference but not on one end of a weak inference? Logically, both make sense: a locked set and an external peer of a related digit cannot both be true so the weak inference is totally fine.
If one wishes to limit the available object types in inferences to single digits then the ALS strong inferences can be written that way (though less compactly). For instance:
ALS[(6)r8c1=(7)r8c16] - ALS[(7)r8c2=(6)r68c2]
In this way there would never be any "extraneous" digits cluttering up ones weak inference notations.
Personally, I only care if the logic is valid so have no problem either way. I am only perplexed by the idea that somehow what is fine in strong inference notation is not fine in weak inference notation, or vice versa. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Sat Dec 17, 2011 2:22 am Post subject: |
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Withdrawn: Not sure of some points being accurate.
Last edited by daj95376 on Sat Dec 17, 2011 3:10 pm; edited 1 time in total |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sat Dec 17, 2011 4:56 am Post subject: |
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| Asellus wrote: | | Just to satisfy my curiosity... Why would someone consider it fine to notate a locked set object on one end of a strong inference but not on one end of a weak inference? Logically, both make sense: a locked set and an external peer of a related digit cannot both be true so the weak inference is totally fine. |
If you prefer a Boolean outlook of the AIC, there is little difference. However, I take the 'I' of AIC a bit more literally and prefer the "inference stream" outlook. In this case, the weak inference involves only one digit, while each strong inference involves two cells. More accurately, each derived strong inference involves the native strong inference sets of two cells. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Dec 17, 2011 11:41 am Post subject: |
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| ronk wrote: | | If you prefer a Boolean outlook of the AIC, there is little difference. |
Ah... then I definitely prefer the Boolean outlook, with the sky being the limit on the nature of the objects on either end of either sort of inference. "Native Inference" is new jargon to me. Perhaps if it were called an "ANIC" I'd agree that literalness was evident in the restrictions. And I can't see that either approach is more or less "streamy" than the other. I must be uninitiated (unbaptized?). To me, "chain" or "stream" just seem to be metaphors for "sequence" ... though stream opens up the possibility of involving fish, I suppose! Anyway, I am often baffled by what I see as a propensity for overly restrictive definitions in this curious sudoku world. |
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ronk
Joined: 07 May 2006
Posts: 398
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| Posted: Sat Dec 17, 2011 12:56 pm Post subject: |
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| Asellus, had I expected a cynical response, I wouldn't have bothered to answer your question. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sun Dec 18, 2011 4:33 am Post subject: |
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| ronk wrote: | | Asellus, had I expected a cynical response, I wouldn't have bothered to answer your question. |
Not cynical... a failed attempt, it seems, at lighthearted humor. If you felt ridiculed, I apologize. There was no such intent. |
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