25 Dec 2006 Nightmare: "Unique" XYZ Wing
Posted: Tue Dec 26, 2006 10:05 pm
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:
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 "^"):
Code: Select all
.---------------------.------------------.------------------.
| 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 |
'---------------------'------------------'------------------'
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