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4/26/07 Daily Nightmare

 
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rep'nA
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Joined: 19 Jan 2007
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Location: Union City, California

PostPosted: Thu Apr 26, 2007 12:23 am    Post subject: 4/26/07 Daily Nightmare Reply with quote

After some singles, one gets to

Code:

.---------------.---------------.---------------.
| 4    8    13  | 16   7    5   | 369  2    369 |
| 9    26   7   | 246  346  2468| 1    358  3568|
| 13   26   5   | 9    136  1268| 368  7    4   |
:---------------+---------------+---------------:
| 8    37-  6   | 25*  9    27* | 4    1    35* |
| 5    1379 134*| 8    14*  147*| 379- 6    2   |
| 2    179  14  | 1456 1456 3   | 5789 589  589 |
:---------------+---------------+---------------:
| 7    4    8   | 3    156  169 | 2    59   1569|
| 6    135  9   | 7    2    14  | 358  3458 1358|
| 13   135  2   | 1456 8    1469| 3569 3459 7   |
'---------------'---------------'---------------'


The 6 cells in r4c569, r5c356 contain the candidates (1,2,3,4,5,7) with max multiplicity (1,1,2,1,1,1). Therefore, subset counting (or the ALS xz-rule) tells you that you can remove 3 from r4c2 and r5c7, solving the puzzle.

Alternatively, consider the broken wing pattern on 1

Code:

 *-----------------------------------------------------------*
 | 4     8     13*   | 16*   7     5     | 369   2     369   |
 | 9     26    7     | 246   346   2468  | 1     358   3568  |
 | 13*   26    5     | 9     136   1268  | 368   7     4     |
 |-------------------+-------------------+-------------------|
 | 38    37    6     | 25    9     27    | 4     1     358   |
 | 5     1379  134   | 8     14    147   | 379   6     2     |
 | 2     179-  14    | 1456& 1456  3     | 5789  589   589   |
 |-------------------+-------------------+-------------------|
 | 7     4     8     | 3     156   169   | 2     59    1569  |
 | 6     135   9     | 7     2     14    | 358   3458  1358  |
 | 13*   135&  2     | 1456* 8     1469& | 3569  3459  7     |
 *-----------------------------------------------------------*



with guardians in r6c4 and r9c26. r6c2=1 knocks out the guardians in r6c4 and r9c2. Moreover, r6c2=1 => r9c1=1, killing the guardian in r9c6. Therefore, r6c2<>1, and after the applying the uncovered naked quad in row 6, the puzzle is solved.
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Ron Moore
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Joined: 13 Aug 2006
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PostPosted: Thu Apr 26, 2007 1:56 am    Post subject: Reply with quote

You can also use some smaller ALS's to eliminate (7)r4c6 with the ALS XZ rule, which solves the puzzle quickly:

(7=3)r4c2 - (3=147)r5c356 => r4c6 <> 7
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rep'nA
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Joined: 19 Jan 2007
Posts: 49
Location: Union City, California

PostPosted: Thu Apr 26, 2007 11:08 am    Post subject: Reply with quote

Ron Moore wrote:
You can also use some smaller ALS's to eliminate (7)r4c6 with the ALS XZ rule, which solves the puzzle quickly:

(7=3)r4c2 - (3=147)r5c356 => r4c6 <> 7


Very nice Ron. I don't know how I missed it, I was right there.
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