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5 May 2007

 
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Ron Moore
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Joined: 13 Aug 2006
Posts: 72
Location: New Mexico

PostPosted: Mon May 28, 2007 2:43 pm    Post subject: 5 May 2007 Reply with quote

Start position for the 5 May 2007 Nightmare:

Code:

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


My solution coincided with the Sudocue solver's through these major steps:
    Naked quad, digits 2,4,8,9 in r2345c5

    Naked quad, digits 2,5,6,7 in r89c12

    Hidden pair, digits 1,8 in r12c2

    Skyscraper, digit 7 -- (7): r5c3 = r1c3 - r1c8 = r6c8 => r5c9, r6c1 <> 7

    Sue de Coq, box 3, column 8:
      Set C (line/box intersection) = r12c8, candidates 1,2,7,9
      Set A (box) = r2c7, candidates 7,9
      Set B (line) = r7c8, candidates 1,2
After these steps, the grid is:

Code:

-------------------------------------------------------------
| 3479  18    3479 |  6      5      248  |  123    B1279  B24   |
| 6     18    349  |  29     2489   7    |  1235   B129   B245  |
| 4579  579   2    |  3      49     1    | B79      8      6    |
------------------+---------------------+----------------------
| 8     2379  6    |  279    249    234  |  279     5      1    |
| 1     2379  379  |  2579   289    2358 |  4       6      28   |
| 29    4     5    |  1279   16     268  |  2789    79     3    |
------------------+---------------------+----------------------
| 349   39    349  | A125    7     A256  |  12568  C12    *28-5 |
| 257   2567  1    |  8      3      256  |  256     4      9    |
| 25    256   8    |  4     A16     9    |  1256    3      7    |
-------------------------------------------------------------


With the "table conflict" and "table verity" techniques disabled, the Sudocue solver continues from this position with (not in order): a finned jellyfish, an XY wing, an XYZ wing, an empty rectangle, a skyscraper, 5 XY chains, and 4 ALS XZ rule eliminations. After some optimization of my initial solution, I found that the puzzle could be completed with one major step.

I don't think it's particularly important, but for those who like to classify according to conventionally defined patterns, the AIC below represents an ALS XY wing elimination. For more info on that pattern, see http://www.sudopedia.org/wiki/ALS-XY-Wing. The sets of cells A, B, and C used in that formulation are identified with corresponding prefixes in the diagram. These are precisely the sets of cells for the first, third, and second nodes, respectively, of the AIC:
    (5=162)r7c46|r9c5 - (2=1)r7c8 - (1=24795)r12c89 => r7c9 <> 5
After this elimination, the puzzle is completed with singles and one naked pair.
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