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Ron Moore

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

Posted: Fri Dec 22, 2006 10:35 pm    Post subject: 17 Dec 2006 Nightmare

My solution coincided with the Sudocue solver's to this point:
 Code: .-------------------.------------------.------------------. | 3      6     2    | 8     14579 15   | 459   49    457  | |*89     7    *89   | 46    456   2    | 3     1     456  | | 4      1     5    | 679   3679  36   | 27    289   2678 | :-------------------+------------------+------------------: | 2      5     478  | 17    1378  9    | 6     348   348  | | 1      3     489  | 26    268   468  | 459   7     2458 | |*89+7  *89    6    | 5     2378  348  | 49    23489 1    | :-------------------+------------------+------------------: | 56-7   2     37   | 146   1456  15   | 8     34    9    | | 689    4     1    | 3     689   68   | 27    5     27   | | 589   *89   *89+3 | 249   24589 7    | 1     6     34   | '-------------------'------------------'------------------'

Here there is a 6-cell deadly pattern based on "89" looming in r2c13|r6c12|r9c23 (marked with "*"). There are only two possible escapes, the surplus candidates (7)r6c1 and (3)r9c3, and each of these possibilities quickly leads to the common conclusion, r7c1 <> 7.
(7=89)r6c12 - DP[r2c13|r6c12|r9c23] - (89=3)r9c23 - (3=7)r7c3 => r7c1 <> 7.
After this, r6c1 solves as "7" and r4c3 reduces to "48", so there is an XY wing in r4c3, r6c27which eliminates (4)r4c8. (This can be seen even in the diagrammed position, using the ALS r4c3|r6c12). With basic follow up, we reach this position:
 Code: .---------------.---------------.-----------------. | 3    6    2   | 8    79   1   |*49+5 *49   -57  | | 89   7    89  | 4    5    2   | 3     1     6   | | 4    1    5   | 69   3679 36  | 27    29    8   | :---------------+---------------+-----------------: | 2    5    4   | 7    1    9   | 6     8     3   | | 1    3    89  | 26   268  468 | 459   7     25  | | 7    89   6   | 5    238  348 |*49   *49+2  1   | :---------------+---------------+-----------------: | 6    2    7   | 1    4    5   | 8     3     9   | | 89   4    1   | 3    689  68  | 27    5     27  | | 5    89   3   | 29   289  7   | 1     6     4   | '---------------'---------------'-----------------'

The solution is nearly complete, and one way to finish it off is to use the "49" UR pattern in r16c78 (marked with "*"). The situation is somewhat like an XY wing, with the UR serving as the pivot instead of a single cell:
(5=2)r5c9 - (2=49)r6c78 - UR - (49=5)r1c78 => r1c9 <> 5.
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