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27 Dec 2006 Nightmare

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

PostPosted: Thu Dec 28, 2006 5:58 pm    Post subject: 27 Dec 2006 Nightmare Reply with quote

This is the position in the 27 Dec 2006 Nightmare, after initial eliminations from basic techniques, a "134" naked triple in r1c123, a "1569" naked quad in r1236c6, and a swordfish in rows 1,4,9 for digit "7":
Code:

.------------------.------------------.------------------.
| 13    134   134  | 59    6     579  | 8     29    257  |
| 5     68    2    | 38    179   4    | 679   1369  136  |
| 9     68    7    | 38    15    2    | 56    136   4    |
:------------------+------------------+------------------:
|*78    2     4589 | 569   59    3    | 1     468   567  |
| 6     135   1358 | 7     4     15   | 25    238   9    |
| 13    13457 13459| 2     8     1569 | 567   346   356  |
:------------------+------------------+------------------:
|*28    15    1568 | 4    *259   569  | 3     7     1268 |
| 4     1357  1356 | 156  *257   8    | 269   1269  126  |
| 2-78  9     168  | 16    3    *67   | 4     5     1268 |
'------------------'------------------'------------------'

As an alternative to the Sudocue solver's solution path from this point, I suggest continuing to work on the "7's" with this chain (cells marked with "*"):
    (7=8)r4c1 - (8=2)r7c1 - (2)r7c5 = (2-7)r8c5 = (7)r9c6 => r9c1 <> 7
This enables us to place all "7's" in the grid, which reduces to the following position:
Code:

.---------------.---------------.----------------.
| 13   134  14  | 59   6    59  | 8    2     7   |
| 5    68   2   | 38   7    4   | 69   1369  136 |
| 9    68   7   | 38   1    2   | 5    36    4   |
:---------------+---------------+----------------:
| 7    2    4589| 569  59   3   | 1    468   56  |
| 6    135  158 | 7    4    15  | 2    38    9   |
| 13   1345 1459| 2    8    1569| 7    346   356 |
:---------------+---------------+----------------:
|*28   15   156 | 4    29   69  | 3    7    *1268|
| 4    7    3   | 156  25   8   | 69   169   126 |
|*28   9    16  | 16   3    7   | 4    5    *28  |
'---------------'---------------'----------------'

From the "28" UR pattern in r79c19 (marked with "*"), there is a "unique corner" elimination of (28)r7c9, reducing r7c9 to "16". This then creates a "156" naked triple in r7c239, and after the resulting eliminations the rest is easy. (There's no need to make explicit use of the "569" triple in r4c459.)
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