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maximum number of candidates after removal singles

 
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soduko

Joined: 10 Oct 2005
Posts: 50
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PostPosted: Fri Jul 03, 2009 12:56 pm    Post subject: maximum number of candidates after removal singles Reply with quote

Hi,

Does anybody know the maximum number of candidates that a valid soduko can have after naked and hidden singles are removed?
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strmckr

Joined: 24 Apr 2009
Posts: 52
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PostPosted: Sat Jul 04, 2009 3:15 am    Post subject: Reply with quote

Code:
1 2 3 | 4 5 6 | 7 8 9
 4 5 6 | 7 8 9 | 1 2 3
 7 8 9 | 1 3 2 | 5 6 4
-------+-------+-------
 2 3 . | 9 . 5 | 8 . 6
 6 . 5 | 2 . 8 | 9 3 .
 8 9 7 | 3 6 1 | 2 4 5
-------+-------+-------
 3 6 2 | 5 1 7 | 4 9 8
 5 . 8 | 6 9 4 | 3 . 2
 9 . . | 8 2 3 | 6 5 .


70 is the conjectured max,

this puzzle is from gsf.
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daj95376

Joined: 05 Feb 2006
Posts: 349
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PostPosted: Sat Jul 04, 2009 3:21 am    Post subject: Reply with quote

I believe this might be a possible candidate.

Code:
# Easter Monster

 +-----------------------+
 | 1 . . | . . . | . . 2 |
 | . 9 . | 4 . . | . 5 . |
 | . . 6 | . . . | 7 . . |
 |-------+-------+-------|
 | . 5 . | 9 . 3 | . . . |
 | . . . | . 7 . | . . . |
 | . . . | 8 5 . | . 4 . |
 |-------+-------+-------|
 | 7 . . | . . . | 6 . . |
 | . 3 . | . . 9 | . 8 . |
 | . . 2 | . . . | . . 1 |
 +-----------------------+

 +--------------------------------------------------------------------------------+
 |  1       478     34578   |  3567    3689    5678    |  3489    369     2       |
 |  238     9       378     |  4       12368   12678   |  138     5       368     |
 |  23458   248     6       |  1235    12389   1258    |  7       139     3489    |
 |--------------------------+--------------------------+--------------------------|
 |  2468    5       1478    |  9       1246    3       |  128     1267    678     |
 |  234689  12468   13489   |  126     7       1246    |  123589  12369   35689   |
 |  2369    1267    1379    |  8       5       126     |  1239    4       3679    |
 |--------------------------+--------------------------+--------------------------|
 |  7       148     14589   |  1235    12348   12458   |  6       239     3459    |
 |  456     3       145     |  12567   1246    9       |  245     8       457     |
 |  45689   468     2       |  3567    3468    45678   |  3459    379     1       |
 +--------------------------------------------------------------------------------+
 # 179 eliminations remain
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