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A Grouped M-wing

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Tue Jul 06, 2010 12:58 am    Post subject: A Grouped M-wing Reply with quote
Code:
Puzzle: M3886622sh(11)
+-------+-------+-------+
| 7 . 9 | . . . | 3 . 4 |
| 2 . . | 6 . . | . . 7 |
| . 5 . | 9 . . | . 8 . |
+-------+-------+-------+
| . . . | 3 9 . | . . . |
| . . . | 1 . 2 | . . . |
| 9 3 . | . 5 6 | . 1 2 |
+-------+-------+-------+
| . 2 . | . . 9 | . 7 . |
| 5 . . | . . 4 | . . 1 |
| 8 . 7 | . . . | 9 . 3 |
+-------+-------+-------+


After basics:
Code:
+----------------+----------------+----------------+
| 7    6    9    | 258  128  158  | 3    25   4    |
| 2    8    13   | 6    4    35   | 15   9    7    |
| 134  5    134  | 9    27   37   | 12   8    6    |
+----------------+----------------+----------------+
| 146  147  2    | 3    9    78   | 4568 456b 58   |
| 46   47   5    | 1    78   2    | 468  3    9    |
| 9    3    8    | 4    5    6    | 7    1    2    |
+----------------+----------------+----------------+
| 134  2    1346 | 58   136  9    | 46a  7    58   |
| 5    9    36   | 7    2368 4    | 2-68 26c  1    |
| 8    14   7    | 25   126  15   | 9   2456d 3    |
+----------------+----------------+----------------+

If a is 4, b is 4.

If b is not 6, one of cd is 6. a and cd are pincers on 6, making the elimination of 6 in R8C7.

Not that this helps very much!

My question is, this looks like a cycle. Are there other eliminations to be made in this grouped chain / loop?

Keith
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Tue Jul 06, 2010 6:27 am    Post subject: Re: A Grouped M-wing Reply with quote
keith wrote:
My question is, this looks like a cycle. Are there other eliminations to be made in this grouped chain / loop?

I believe the weak inference in [r4c8] also results in an elimination.

Code:
(6=4)r7c7 - (4)r45c7 = (4-6)r4c8 = (6)r89c8 - loop  =>  r4c8<>5, r8c7<>6

[Edit: corrected one typo. Thanks Mogulmeister! Then caught another typo as well.]

Last edited by daj95376 on Tue Jul 06, 2010 4:38 pm; edited 2 times in total
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Mogulmeister



Joined: 03 May 2007
Posts: 1151
PostPosted: Tue Jul 06, 2010 8:08 am    Post subject: Reply with quote
Did you mean r7c7 at the start of that chain Danny ?
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ronk



Joined: 07 May 2006
Posts: 398
PostPosted: Tue Jul 06, 2010 8:55 am    Post subject: Re: A Grouped M-wing Reply with quote
daj95376 wrote:
keith wrote:
My question is, this looks like a cycle. Are there other eliminations to be made in this grouped chain / loop?

I believe the weak inference in [r4c8] also results in an elimination.

Code:
(6=4)r7c8 - (4)r4c7 = (4-6)r4c8 = (6)r89c8 - loop  =>  r4c8<>5, r8c7<>6

Four different m-rings exist simultaneously, all resulting in r4c8=46, r8c7<>6.

(6=4)r7c7 - (4)r789c8 = (4-6)r4c8 = (6)r456c7 - loop
(4=6)r7c7 - (6)r789c8 = (6-4)r4c8 = (4)r456c7 - loop
(4=6)r7c7 - (6)r789c8 = (6-4)r4c8 = (4)r789c8 - loop
(4=6)r7c7 - (6)r456c7 = (6-4)r4c8 = (4)r456c7 - loop

All possible candidate positions are listed.
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Tue Jul 06, 2010 5:02 pm    Post subject: Re: A Grouped M-wing Reply with quote
ronk wrote:
Four different m-rings exist simultaneously, all resulting in r4c8=46, r8c7<>6.

(6=4)r7c7 - (4)r789c8 = (4-6)r4c8 = (6)r456c7 - loop
(4=6)r7c7 - (6)r789c8 = (6-4)r4c8 = (4)r456c7 - loop
(4=6)r7c7 - (6)r789c8 = (6-4)r4c8 = (4)r789c8 - loop
(4=6)r7c7 - (6)r456c7 = (6-4)r4c8 = (4)r456c7 - loop

All possible candidate positions are listed.

I believe your r4c8=46 is equivalent to my r4c8<>5. That only leaves the question of how many M-Rings exist.
(Exact candidate positions are listed.)

Code:
Loop B (4=6)r7c7 - r45c7 = (6-4)r4c8 = (4)r9c8  - loop  =>  r4c8<>5, r8c7<>6
Loop B (4=6)r7c7 - r89c8 = (6-4)r4c8 = (4)r45c7 - loop  =>  r4c8<>5, r8c7<>6
Loop C (4=6)r7c7 - r89c8 = (6-4)r4c8 = (4)r9c8  - loop  =>  r4c8<>5, r8c7<>6
Loop D (4=6)r7c7 - r45c7 = (6-4)r4c8 = (4)r45c7 - loop  =>  r4c8<>5, r8c7<>6

Loop B (6=4)r7c7 - r45c7 = (4-6)r4c8 = (6)r89c8 - loop  =>  r4c8<>5, r8c7<>6
Loop B (6=4)r7c7 - r9c8  = (4-6)r4c8 = (6)r45c7 - loop  =>  r4c8<>5, r8c7<>6
Loop C (6=4)r7c7 - r9c8  = (4-6)r4c8 = (6)r89c8 - loop  =>  r4c8<>5, r8c7<>6
Loop D (6=4)r7c7 - r45c7 = (4-6)r4c8 = (6)r45c7 - loop  =>  r4c8<>5, r8c7<>6
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ronk



Joined: 07 May 2006
Posts: 398
PostPosted: Tue Jul 06, 2010 5:12 pm    Post subject: Re: A Grouped M-wing Reply with quote
daj95376 wrote:
That only leaves the question of how many M-Rings exist.

Code:
Loop B (4=6)r7c7 - r45c7 = (6-4)r4c8 = (4)r9c8  - loop  =>  r4c8<>5, r8c7<>6
Loop B (4=6)r7c7 - r89c8 = (6-4)r4c8 = (4)r45c7 - loop  =>  r4c8<>5, r8c7<>6
Loop C (4=6)r7c7 - r89c8 = (6-4)r4c8 = (4)r9c8  - loop  =>  r4c8<>5, r8c7<>6
Loop D (4=6)r7c7 - r45c7 = (6-4)r4c8 = (4)r45c7 - loop  =>  r4c8<>5, r8c7<>6

Loop B (6=4)r7c7 - r45c7 = (4-6)r4c8 = (6)r89c8 - loop  =>  r4c8<>5, r8c7<>6
Loop B (6=4)r7c7 - r9c8  = (4-6)r4c8 = (6)r45c7 - loop  =>  r4c8<>5, r8c7<>6
Loop C (6=4)r7c7 - r9c8  = (4-6)r4c8 = (6)r89c8 - loop  =>  r4c8<>5, r8c7<>6
Loop D (6=4)r7c7 - r45c7 = (4-6)r4c8 = (6)r45c7 - loop  =>  r4c8<>5, r8c7<>6

Traversing a loop in two directions doesn't mean there are two loops. The first "loop B" and the fourth "loop B" are for the same loop. Ditto for three other pairs.

daj95376 wrote:
I believe your r4c8=46 is equivalent to my r4c8<>5.

It is. I prefer the "bivalue assignment" notation because it can be deduced from the chain expression without reference to pencilmarks.
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Tue Jul 06, 2010 5:42 pm    Post subject: Re: A Grouped M-wing Reply with quote
ronk wrote:
Traversing a loop in two directions doesn't mean there are two loops. The first "loop B" and the fourth "loop B" are for the same loop. Ditto for three other pairs.

Excellent point! Normally, my chain() sorts out chains/loops with duplicate results; however, I have a special version of chain() that captures and lists all M-Wings, M-Rings, and W-Wings that it encounters. I missed the fact that the M-Rings would be listed twice because of the "loop". Thanks!

BTW: I just recently added your classifications to my output. Do you agree with the labels I attached to the first four loops?

Regards, Danny
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daj95376



Joined: 23 Aug 2008
Posts: 3854
PostPosted: Wed Jul 07, 2010 12:09 am    Post subject: Reply with quote
Note:

The letter next to "Loop" is from a classification/categorization that ronk created for M-Wings and M-Rings in the Players' Forum. They are not sequence designators.

Regards, Danny
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