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25 Dec 2006 Nightmare: "Unique" XYZ Wing

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

PostPosted: Tue Dec 26, 2006 10:05 pm    Post subject: 25 Dec 2006 Nightmare: "Unique" XYZ Wing Reply with quote

This is the position in the 25 Dec 2006 Nightmare, after initial eliminations from basic techniques, a "567" naked triple in r2c689, and a "1267" naked quad in r1236c6:
Code:

.---------------------.------------------.------------------.
| 2356  -3567    257  | 137   4     1267 | 9    67     8    |
|#34    #348     1    | 38    9     67   | 2    567    567  |
| 269    6789    2789 | 5     78    267  | 3    4      1    |
:---------------------+------------------+------------------:
| 8      145     25   | 9     6     3    | 7    125    245  |
| 25-69  15-679  2579 | 4     17    8    | 15   12356 ^2356 |
|^46     1467    3    | 2     5     17   | 148  1-68   9    |
:---------------------+------------------+------------------:
| 7      2       6    | 18    138   4    | 158  9      35   |
| 359   *59+38   4    | 178   2    *59   | 6    1378   37   |
| 1     *59+38   589  | 6     378  *59   | 48   2378   2347 |
'---------------------'------------------'------------------'

Here there is a "unique XYZ wing," in which the surplus candidates 3,8 for the "59" UR pattern in r89c26 (marked with "*") lie in column 2 only. With r2c12 (marked with "#"), they form an XYZ wing pattern which could be used to eliminate (3)r1c2. Unfortunately, this doesn't really seem to advance the solution much.

This 3-D chain leads to a quick finish (start and end cells marked with "^"):
    (6=4)r6c1 - (4=3)r2c1 - (3=786)r2c46|r3c5 - (6)r2c89 = (6)r1c8 - (6)r56c8 = (6)r5c9 => r5c12, r6c8 <> 6
After these eliminations, a "36" hidden pair is present in r5c89, and this is enough to finish the solution easily.
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