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18 March 2007

 
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Ron Moore
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Location: New Mexico

PostPosted: Thu Mar 29, 2007 3:19 pm    Post subject: 18 March 2007 Reply with quote

Start position for the 18 March 2007 Daily Nightmare:

Code:

. 3 .|. 2 .|. . .
9 . .|. . 7|. 2 3
. 4 .|. . .|9 . .
-----+-----+-----
6 . 3|. . 2|. . .
7 . .|5 . 6|. . 2
. . .|4 . .|5 . 6
-----+-----+-----
. . 8|. . .|. 6 .
4 2 .|1 . .|. . 5
. . .|. 9 .|. 8 .

Initial eliminations from basic techniques, and a skyscraper for digit 9 in r5c8, r5c2, r7c2, and r8c3, bring about the position below, in which there are (at least) two useful AIC's.

Code:
.------------------.------------------.------------------.
| 158   3     1567 | 689   2     1459 | 14678 1457  1478 |
| 9     168   156  | 68    1458  7    | 1468  2     3    |
| 1258  4     12567| 368   1358  135  | 9     157   178  |
:------------------+------------------+------------------:
| 6     5     3    | 789   178   2    | 1478  1479  1478 |
| 7     189   4    | 5     138   6    | 138   139   2    |
| 128   189   12   | 4     1378  139  | 5     1379  6    |
:------------------+------------------+------------------:
| 135   17    8    | 237   3457  345  | 124   6     9    |
| 4     2     9    | 1     6     8    | 37    37    5    |
| 135   167   156  | 237   9     345  | 124   8     14   |
'------------------'------------------'------------------'

An AIC which is (in effect) found by the Sudocue solver in a "Medusa Bridge" step is
    (4)r1c8 = (4-9)r4c8 = (9)r4c4 - (9)r1c4 = (9)r1c6 => r1c6 <> 4
There is also this grouped AIC:
    (3=689)r123c4 - (9)r4c4 = (9-3)r6c6 = (3)r56c5 => r3c5 <> 3
After these eliminations no further Medusa steps are needed. After basic follow up, the puzzle is completed with a naked "128" triple in column 1, an X wing for digit 1 in r27c27, then an ER in box 6 for digit 8 which eliminates (8)r4c4.
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Sudtyro
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Joined: 16 Jan 2007
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PostPosted: Sat Mar 31, 2007 2:06 pm    Post subject: Re: 18 March 2007 Reply with quote

Ron Moore wrote:
An AIC which is (in effect) found by the Sudocue solver in a "Medusa Bridge" step is
    (4)r1c8 = (4-9)r4c8 = (9)r4c4 - (9)r1c4 = (9)r1c6 => r1c6 <> 4

Is there an equivalent ALS rule and/or Wing structure that reproduces this elimination?
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Myth Jellies
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Joined: 04 Apr 2006
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PostPosted: Sun Apr 01, 2007 6:06 am    Post subject: Re: 18 March 2007 Reply with quote

Sudtyro wrote:
Ron Moore wrote:
An AIC which is (in effect) found by the Sudocue solver in a "Medusa Bridge" step is
    (4)r1c8 = (4-9)r4c8 = (9)r4c4 - (9)r1c4 = (9)r1c6 => r1c6 <> 4

Is there an equivalent ALS rule and/or Wing structure that reproduces this elimination?


If it helps, this is basically a multi-digit version of 3 Strong Bilocation Links. You have a 4=4 - 9=9 - 9=9 structure where you know one of the endpoints has to be true. Thus, in a way, it belongs to the same family of logic that gives you x-wings, two-tailed kites, and skyscrapers. Of course, an AIC is pattern oriented enough in and of itself.
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Ron Moore
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PostPosted: Tue Apr 03, 2007 4:16 pm    Post subject: Re: 18 March 2007 Reply with quote

Sudtyro wrote:
Ron Moore wrote:
An AIC which is (in effect) found by the Sudocue solver in a "Medusa Bridge" step is
    (4)r1c8 = (4-9)r4c8 = (9)r4c4 - (9)r1c4 = (9)r1c6 => r1c6 <> 4

Is there an equivalent ALS rule and/or Wing structure that reproduces this elimination?

Code:
.------------------.------------------.------------------.
| 158   3     1567 | 689   2     1459 | 14678 1457  1478 |
| 9     168   156  | 68    1458  7    | 1468  2     3    |
| 1258  4     12567| 368   1358  135  | 9     157   178  |
:------------------+------------------+------------------:
| 6     5     3    | 789   178   2    | 1478  1479  1478 |
| 7     189   4    | 5     138   6    | 138   139   2    |
| 128   189   12   | 4     1378  139  | 5     1379  6    |
:------------------+------------------+------------------:
| 135   17    8    | 237   3457  345  | 124   6     9    |
| 4     2     9    | 1     6     8    | 37    37    5    |
| 135   167   156  | 237   9     345  | 124   8     14   |
'------------------'------------------'------------------'


Well, if you'd asked about the second chain, there is an ALS XZ rule elimination for that elimination. A chain representing this view is
    (3=6897)r1234c4 - (7=183)r456c5 => r3c5 <> 3
I'm not sure why I didn't write it this way, other than to say that from other recent work I'm trying to make more use of strong bilocation links in AIC's.

If you're asking if the elimination from the first chain can be obtained from some structure like an ALS XZ or ALS XY wing configuration, or from what some would call a WXYZ wing (or similar configuration with more cells & digits), I can't see anything offhand.
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Sudtyro
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Posts: 49

PostPosted: Wed Apr 04, 2007 12:02 pm    Post subject: Reply with quote

Thanks to MJ and RM for your inputs...
While the AICs are fundamental to nearly all solution techniques, it's always interesting (and helpful) to see any equivalent pattern-based solutions.
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