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Menneske

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Wed Mar 16, 2011 11:19 pm    Post subject: Menneske Reply with quote

This is #5396175, Super hard (26)

Please, tell me there's a mistake in the grid, it'll be better for my self-esteem. Very Happy

I can't do a thing other than a worthless 267 XYZ-Wing which removed 6 from r2c1.

Code:

+-----------------+----------+-------------+
| 458  149  159   | 39 7   6 | 48  234 238 |
| 478  4679 69    | 1  39  2 | 5   347 368 |
| 267  3    26    | 8  5   4 | 67  9   1   |
+-----------------+----------+-------------+
| 49   2    8     | 39 349 5 | 1   6   7   |
| 1    46   3     | 7  46  8 | 2   5   9   |
| 69   5    7     | 2  69  1 | 3   8   4   |
+-----------------+----------+-------------+
| 3    8    259   | 6  1   7 | 49  24  25  |
| 67   167  4     | 5  2   9 | 678 137 368 |
| 2567 1679 12569 | 4  8   3 | 679 127 256 |
+-----------------+----------+-------------+

Play this puzzle online at the Daily Sudoku site
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daj95376



Joined: 23 Aug 2008
Posts: 3854

PostPosted: Thu Mar 17, 2011 12:53 am    Post subject: Reply with quote

Marty: No, it's just a complex grid. My solver used an AIC and 2x XY-Chain.

Single-Stepper:

HoDoKu uses a Death Blossom to crack it open, but my solver guided me to a simple network:

Code:
          (6=7)r3c7 ................
         /                          \
(6)r2c9 - (6=9)r2c3 - (9=3)r2c5 - (37=4)r2c8 - r1c7 = (4-9)r7c7 = r7c3 - (9=6)r2c3 - (6)r2c9
____________________________________________________________________________________________

Which can also be viewed as Kraken Cell r2c8={347}:

Code:
 (3)r2c8 - (3=9)r2c5               - (9=6)r2c3 - (6)r2c9
 (4)r2c8 - r1c7 = (4-9)r1c7 = r7c3 - (9=6)r2c3 - (6)r2c9
 (7)r2c8                           - (7=6)r3c7 - (6)r2c9
 +-----------------------------------------------------------------------+
 |  458    149    159    |  39     7      6      |  48     234    238    |
 |  478    4679   69     |  1      39     2      |  5     {347}   38-6   |
 |  267    3      26     |  8      5      4      |  67     9      1      |
 |-----------------------+-----------------------+-----------------------|
 |  49     2      8      |  39     349    5      |  1      6      7      |
 |  1      46     3      |  7      46     8      |  2      5      9      |
 |  69     5      7      |  2      69     1      |  3      8      4      |
 |-----------------------+-----------------------+-----------------------|
 |  3      8      259    |  6      1      7      |  49     24     25     |
 |  67     167    4      |  5      2      9      |  678    137    368    |
 |  2567   1679   12569  |  4      8      3      |  679    127    256    |
 +-----------------------------------------------------------------------+
 # 65 eliminations remain

Regards, Danny
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Thu Mar 17, 2011 3:41 am    Post subject: Reply with quote

Thanks Danny, I never would have solved that one. Talk about rating inconsistency. This was a 26, but just the other day I easily solved a 29 with two steps. Go figure.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Thu Mar 17, 2011 5:52 am    Post subject: Reply with quote

Marty R. wrote:
Thanks Danny, I never would have solved that one. Talk about rating inconsistency. This was a 26, but just the other day I easily solved a 29 with two steps. Go figure.
Marty,

No one knows, but I believe the Menneske rating is not based on techniques needed to solve the puzzle.

I believe it is based on some heuristic to do with the idea of "back doors". Will a particular candidate in a particular cell solve the puzzle? The simpler the back doors, the lower the rating.

I suppose a back door in a two-candidate cell is less complicated than a back door in a three-candidate cell, for example.

I generally choose Menneske puzzles that are not zero but less than about 20.

Keith
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