5 empty boxes?

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

5 empty boxes?

Postby ab » Tue Apr 25, 2006 5:21 pm

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:
Code: Select all
...|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.
ab
 
Posts: 451
Joined: 06 September 2005

Postby coloin » Tue Apr 25, 2006 6:44 pm

No
Dukuso calculated the best
Code: Select all
XXX
XOO
XOO
had 1960 solutions

which was updated to 1152 solutions with PatmaxDadday
Code: Select all
+---+---+---+
|...|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: 1768
Joined: 05 May 2005

Postby Ocean » Tue Apr 25, 2006 7:09 pm

The possible configurations with empty boxes were also discussed here.

kjellfp wrote:I have now completed an exhaustive search on the form
Code: Select all
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:
Code: Select all
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:
Code: Select all
0X0
XXX
0XX

Therefore we cannot have any of these symmetric box patterns:
Code: Select all
0X0
XXX
0X0

0X0
X0X
0X0
Ocean
 
Posts: 442
Joined: 29 August 2005


Return to General