The New Sudoku Players' Forum

[ab]

do you think it's possible to have a puzzle with 5 empty boxes? if not why not?

I put this mask in my generator:

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...|xxx|...
...|xxx|...
...|xxx|...
-----------
xxx|...|xxx
xxx|...|xxx
xxx|...|xxx
-----------
...|xxx|...
...|xxx|...
...|xxx|...


and it filled the centre box but couldn't fill the corner boxes. This suggests to me that 5 empty boxes is not possible, but of course it doesn't prove anything.

[coloin]

No
Dukuso calculated the best

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XXX
XOO
XOO

had 1960 solutions

which was updated to 1152 solutions with PatmaxDadday

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+---+---+---+
|...|159|268|
|...|368|147|
|...|247|359|
+---+---+---+
|124|...|...|
|387|...|...|
|965|...|...|
+---+---+---+
|241|...|...|
|738|...|...|
|659|...|...|
+---+---+---+

This is the thread, with other successful and unsuccessful permutations.
http://forum.enjoysudoku.com/viewtopic.php?t=1180&postdays=0&postorder=asc&start=0

A more definitive is found
http://forum.enjoysudoku.com/viewtopic.php?t=2553&postdays=0&postorder=asc&start=15

[Ocean]

The possible configurations with empty boxes were also discussed here.

I have now completed an exhaustive search on the form

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00X
0XX
XXX

No Sudoku exists, but there are plenty with only two solutions.

To sum it up, what you have established is that all Sudokus with emtpy boxes belong to (or can be transformed to) one of these six (nonisomorphic) cases:

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0XX  00X  0XX  00X  0XX  00X
XXX  XXX  X0X  XX0  X0X  XX0
XXX  XXX  XXX  XXX  XX0  XX0 

When it comes to symmetric patterns, note that the kjell's configuration is equivalent to:

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0X0
XXX
0XX

Therefore we cannot have any of these symmetric box patterns:

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0X0
XXX
0X0

0X0
X0X
0X0