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Ron Moore

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

Posted: Sun Dec 03, 2006 5:14 pm    Post subject: 26 Nov 2006, 2 x 4 Deadly Pattern

I found a 2-row by 4-column deadly pattern in the 26 Nov 2006 Nightmare. My solution path was fairly close to the Sudocue solver to this point:

 Code: .---------------.---------------.---------------. | 3458 39   2   | 1458 1479 5789| 6    349  3479| | 1    45   49  | 2456 3    567 | 479  24   8   | | 348  7    6   | 248  249  89  | 5    1    2349| :---------------+---------------+---------------: | 457  45   19  | 3    68   2   | 19   58   467 | | 3457 2    34  | 9    68   1   | 47   58   467 | | 6    19   8   | 7    5    4   | 2    39   139 | :---------------+---------------+---------------: | 9    36   134 | 248  247  378 | 14   246  5   | | 24   8    5   | 1246 1249 69  | 3    7    1249| | 234  136  7   | 1245 1249 359 | 8    2469 1249| '---------------'---------------'---------------'

Here I continued with a grouped chain:

(4=5)r4c2 - (5=497)r2c237 - (7=4)r5c7 => r5c13 <> 4

Following this up, r5c3 solves as "3", r5c1 reduces to "57"; r7c3 reduces to "14" which forms a naked pair "14" with r7c7, which (among other reductions) eliminates "4" from r7c8. Then we have an XY chain (actually an XY ring):

(4=9)r2c3 - (9=3)r2c1 - (3=6)r7c2 - (6=2)r7c8 - (2=4)r2c8 => r2c2, r2c7 <> 4

Following this up, the grid becomes:

 Code: .---------------.---------------.---------------. | 348  39   2   | 1458 1479 5789| 6    349  3479| | 1    5    49  | 246  3    67  | 79   24   8   | | 348  7    6   | 248  249  89  | 5    1    2349| :---------------+---------------+---------------: |*57   4    19  | 3   *68   2   | 19  *58  *67  | |*57   2    3   | 9   *68   1   | 47  *58  *67+4| | 6    19   8   | 7    5    4   | 2    39   139 | :---------------+---------------+---------------: | 9    36   14  | 28   27   378 | 14   26   5   | | 24   8    5   | 1246 1249 69  | 3    7    1249| | 234  136  7   | 1245 1249 359 | 8    2469 1249| '---------------'---------------'---------------'

In r45c1859 (marked with "*") we have a 75-58-86-67 deadly pattern looming, and r5c9 is the only cell with a surplus candidate, namely "4". So r5c9=4 ("unique corner"), and it's easy from there.
GreenLantern
Regular

Joined: 30 May 2006
Posts: 14

 Posted: Sun Dec 03, 2006 9:13 pm    Post subject: Neat solution! I don't find such large deadly patterns that easily on my own, so I appreciate good examples of them. By the way, there were several other eliminations in your XY-ring in addition to r2c27<>4: r2c4<>4,r9c2<>3, and r9c8<>2.
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