
SudoCue Users A forum for users of the SudoCue programs and the services of SudoCue.Net

View previous topic :: View next topic 
Author 
Message 
Sudtyro Hooked
Joined: 16 Jan 2007 Posts: 49

Posted: Sun Aug 05, 2007 1:50 pm Post subject: 7/8/07 Nightmare...a nice multiplemethods example 


After basics:
Code:  
135 14 345  6 7 2  349 8 49
9 26 7  13 8 134  5 34 26
38 26 348  5 9 34  267 27 1
++
367 8 2  137 4 136  139 39 5
36 5 1  9 36 8  24 24 7
4 79 39  137 2 5  13 6 8
++
1578 3 589  4 156 69  26789 279 26
178 1479 6  2 13 39  4789 5 49
2 49 459  8 56 7  469 1 3
 
A check of the singledigit grids leads to...
Grouped Turbot chain (labels ah in Grid 1 below):
(3): r5c1 = r5c5 – r8c5 = r8c6 – r3c6 = r2c46 – r2c8
= r1c7 => r1c1 <> 3, or
= r4c8 => r4c1 <> 3.
Code:  Grid 1
3* . 3  . . .  3h . .
. . .  3f . 3f  . 3g .
3 . 3  . . 3e  . . .
++
3* . .  3 . 3  3 3h .
3a . .  . 3b .  . . .
. . 3  3 . .  3 . .
++
. . .  . . .  . . .
. . .  . 3c 3d  . . .
. . .  . . .  . . . 
Finned XWing (labels x and f in Grid 2 below):
XWing = r24c48 with r6c4 = fin => r4c6 <> 3,
or grouped Turbot fish:
(3): r46c4 = r2c4 – r2c8 = r4c8 => r4c6 <> 3.
Code:  Grid 2
. . 3  . . .  3 . .
. . .  3x . 3  . 3x .
3 . 3  . . 3  . . .
++
. . .  3x . 3*  3 3x .
3 . .  . 3 .  . . .
. . 3  3f . .  3 . .
++
. . .  . . .  . . .
. . .  . 3 3  . . .
. . .  . . .  . .  .
After followup:
Code:  
15 14 345  6 7 2  349 8 49
9 26 7  13 8 134  5 34 26
38 26 348  5 9 34  267 27 1
++
67 8 2  173* 4 16  139 39 5
36 5 1  9 36 8  24 24 7
4 79 39  137 2 5  13 6 8
++
1578 3 589  4 156 69  26789 279 26
178 1479 6  2 13 39  4789 5 49
2 49 459  8 56 7  469 1 3
 
At this point, multidigit methods abound for a single elimination (r4c4 <> 3):
1. WXYZWing: W=6 and Z=3, using cells (36)r5c5 and (1369)r4c678 => r4c4 <> 3.
2. ALSXZ rule:
ALS(A=[r5c5], B=[r4c678], X=6, Z=3) => r4c4 <> 3.
3. Grouped AIC:
(3=6)r5c5 – (6=193)r4c678 => r4c4 <> 3,
equivalent to both the WXYZWing and the ALSXZ rule.
4. Subset Counting: subset is (36)r5c5 and (1369)r4c678, with digit 3 having multiplicity of 2; all others have multiplicity of 1. Cell r4c4 = 3 would reduce total subset multiplicity from 5 to 3, which is one less than cell count => r4c4 <> 3.
5. APE (Aligned Pair Exclusion): cells (137)r4c4 and (16)r4c6 generate the two pair combinations, 31 and 36, and neither one is allowed => r4c4 <> 3.
6. Nongrouped AIC’s:
(3)r5c5 = (36)r5c1 = (67)r4c1 = (7)r4c4 => r4c4 <> 3.
(3=6)r5c5  (6)r4c6 = (67)r4c1 = (7)r4c4 => r4c4 <> 3.
7. 3D Coloring: Coloring of digits in either of the above AICs quickly shows that (3)r5c5 and (7)r4c4 have opposite colors (parity) => r4c4 <> 3.
8. Discontinuous Nice loops:
[r4c4]3[r5c5]=3=[r5c1]=6=[r4c1]=7=[r4c4] => r4c4 <> 3.
[r4c4]3[r5c5]6[r4c6]=6=[r4c1]=7=[r4c4] => r4c4 <> 3.
These loops are equivalent to the above two nongrouped AIC’s.
Would anyone care to add to this “methods” list for the r4c4 <> 3 elimination? Contributions welcome! 

Back to top 


rep'nA Hooked
Joined: 19 Jan 2007 Posts: 49 Location: Union City, California

Posted: Sun Aug 05, 2007 11:17 pm Post subject: Re: 7/8/07 Nightmare...a nice multiplemethods example 


Sudtyro wrote: 
Would anyone care to add to this “methods” list for the r4c4 <> 3 elimination? Contributions welcome! 
The cells (5,5), (4,6), (4,7), (4,8) could be viewed as an almost xychain, or one could also view the elimination as coming from one of Denis Berthier's xyztchains. I think his notation would look something like:
{3 6}  {6 1}  {1 9 (3#1)}  {9 3}. _________________ "Obviousness is always the enemy to correctness."Bertrand Russell 

Back to top 


Sudtyro Hooked
Joined: 16 Jan 2007 Posts: 49

Posted: Mon Aug 06, 2007 8:28 pm Post subject: Re: 7/8/07 Nightmare...a nice multiplemethods example 


rep'nA wrote: 
The cells (5,5), (4,6), (4,7), (4,8) could be viewed as an almost xychain ... 
Thanks, rep'nA, for the feedback! I've learned just enough about "almost" structures from some of Ron Moore's postings to be almost dangerous , but I'm not sure about an almost xychain. Can you show how that would work with the cells you listed? 

Back to top 


rep'nA Hooked
Joined: 19 Jan 2007 Posts: 49 Location: Union City, California

Posted: Mon Aug 06, 2007 10:31 pm Post subject: Re: 7/8/07 Nightmare...a nice multiplemethods example 


Sudtyro wrote:  rep'nA wrote: 
The cells (5,5), (4,6), (4,7), (4,8) could be viewed as an almost xychain ... 
Thanks, rep'nA, for the feedback! I've learned just enough about "almost" structures from some of Ron Moore's postings to be almost dangerous , but I'm not sure about an almost xychain. Can you show how that would work with the cells you listed? 
Almost xychains are described here and a proof of their general applicability is given here.
In this case, there are two ways to think of the cells above as an almost xychain, one based on the approach given in the above links and one more in the spirit of Ron (and Carcul before him). I'll briefly describe them both. First, if it wasn't for the 3 in r4c7, then we would have an xychain in the cells I described. But since the 3 in r4c7 does not change the max multiplicity of 3 in the chain, it can be added without affecting the conclusions. Frankly, it is just subset counting on a particularly easy to spot pattern.
The second way to think about it is as follows: If the 3 wasn't in r4c7, we would have an xychain and conclude that r4c4<>3. If r4c7=3, then r4c4<>3. This is what I think is the more traditional meaning of an 'almost pattern'. However, since the pattern I use above is more common, I stole the name so that it might be used once in a while. _________________ "Obviousness is always the enemy to correctness."Bertrand Russell 

Back to top 


Sudtyro Hooked
Joined: 16 Jan 2007 Posts: 49

Posted: Tue Aug 07, 2007 10:50 am Post subject: 


Thanks again...good explanation! I hadn't seen your threads in the other forum.
In Ron's jargon, (3)r4c7 must be the "spoiler" digit in the "almost" pattern, and in this case is more like the fin in a finned fish because the spoiler can see the victim cell. I'm guessing the AIC (in Ron's notation) would be something like:
[XYChain r5c5r4c678] = (3)r4c7 => r4c4 <> 3.
Another interesting "method" to add to the list! 

Back to top 




You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot vote in polls in this forum

Powered by phpBB © 2001, 2005 phpBB Group
