5 empty boxes?

Everything about Sudoku that doesn't fit in one of the other sections

5 empty boxes?

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|...|xxxxxx|...|xxxxxx|...|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.
ab

Posts: 451
Joined: 06 September 2005

No
Dukuso calculated the best
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`XXXXOOXOO `

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
Last edited by coloin on Thu Apr 27, 2006 3:00 pm, edited 1 time in total.
coloin

Posts: 1877
Joined: 05 May 2005

The possible configurations with empty boxes were also discussed here.

kjellfp wrote: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.

Ocean wrote: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 XXX0XX `

Therefore we cannot have any of these symmetric box patterns:
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`0X0 XXX0X0 0X0 X0X0X0`
Ocean

Posts: 442
Joined: 29 August 2005