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22 Dec 2006 Nightmare: Another Uniqueness Solution

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

PostPosted: Fri Dec 22, 2006 5:41 pm    Post subject: 22 Dec 2006 Nightmare: Another Uniqueness Solution Reply with quote

I followed the same solution path as the Sudocue solver to this point:
Code:

.-------------------.---------------------.------------------.
| 1      8     49   | 349     349   5     | 2     6     7    |
|#49     7     2    | 1       6     49    | 58    358   38   |
| 3      6     5    | 8       27    27    | 1     9     4    |
:-------------------+---------------------+------------------:
|#249    5     1    | 7       2349  249   | 6     38    389  |
|#2469   2349  8    | 234-69  1     24-69 | 57    57    39   |
|*67+9  ^39   *67+3 |^369     5     8     | 4     2     1    |
:-------------------+---------------------+------------------:
| 5      1     49   | 249     2479  3     | 789   78    6    |
|*67+29  29   *67   | 69      8     1     | 3     4     5    |
| 8      349   36   | 5       479   4679  | 79    1     2    |
'-------------------'---------------------'------------------'


There are some eliminations which can be made from the "38" UR pattern in r24c89 and the "85-57-78" base pattern in r257c78, but they aren't really needed. A uniqueness argument using the "67" UR pattern in r68c13 (marked with "*") is enough to complete the solution with only basic techniques needed thereafter.

In the jargon of the Solving Guide, there are two "unique subset" possibilities here, one of which must hold, but I'll state the argument in equivalent terms of Almost Locked Sets (ALS's). If the UR pattern is avoided by choosing one of the surplus candidates in row 6, either (9)r6c1 or (3)r6c3, the ALS r6c24 (marked with "^") becomes locked with "6" forced into r6c4. On the other hand, if the UR pattern is avoided by choosing one of (2or9)r8c1, then the ALS r245c1 (marked with "#") becomes locked with "6" forced into r5c1. In either case, both of r5c46 see a "6" (and for that matter, so do cells r6c13). In AIC form:

(6=39)r6c24 - ((3or9)=67)r6c13 - UR - (67=(2or9))r8c13 - (249=6)r245c1 => r5c46, r6c13 <> 6
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