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21 Dec 2006 Nightmare Not So Tough

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

PostPosted: Thu Dec 21, 2006 4:34 am    Post subject: 21 Dec 2006 Nightmare Not So Tough Reply with quote

This one's fairly easy if you notice early on an AIC for digit "6".

Code:

.---------------------.---------------------.---------------------.
| 1367   2      13567 | 147    9      8     | 147    145-6  1456  |
| 17     57     4     | 3      6      12    | 179    1259   8     |
| 9     #67     8     | 5      247    124   | 147    3     *1246  |
:---------------------+---------------------+---------------------:
| 5     *46789  2     |#14679  47     3     | 1489   1489   14    |
| 14678  46789  1679  | 124679 2457   12469 | 13489  124589 12345 |
| 14     3      19    | 8      245    1249  | 6      12459  7     |
:---------------------+---------------------+---------------------:
| 37     1      37    |*46     8      5     | 2     #46     9     |
| 2      4689   69    | 469    3      7     | 5      1468   14-6  |
| 468    45689  569   | 2469   1      2469  | 348    7      34-6  |
'---------------------'---------------------'---------------------'

Cells in the chain are alternately marked with "*" and "#". In Eureka notation:

    (6): r3c9 = r3c2 - r4c2 = r4c4 - r7c4 = r7c8 => r1c8, r89c9 <> 6

Following up these eliminations with basic techniques brings the grid to:

Code:

.---------------------.---------------------.---------------------.
| 1367   2      13567 | 147    9      8     | 147    145    56    |
|*17     57     4     | 3      6     *12    | 179    1-259  8     |
| 9     *67     8     | 5     -247    1-24  | 147    3     *26    |
:---------------------+---------------------+---------------------:
| 5      46789  2     | 14679  47     3     | 1489   1489   14    |
| 14678  46789  1679  | 124679 2457   12469 | 3      124589 25    |
| 14     3      19    | 8      245    1249  | 6      12459  7     |
:---------------------+---------------------+---------------------:
| 37     1      37    | 46     8      5     | 2      46     9     |
| 2      4689   69    | 469    3      7     | 5      1468   14    |
| 468    45689  569   | 2469   1      2469  | 48     7      3     |
'---------------------'---------------------'---------------------'

After eliminations from this short XY chain (marked with "*"), only basic techniques are needed to finish the puzzle:

    (2=1)r2c6 - (1=7)r2c1 - (7=6)r3c2 - (6=2)r3c9 => r2c8, r3c56 <> 2.
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