Empty Boxes - I

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

Postby coloin » Wed Sep 13, 2006 12:22 am

Our minimum B159 with 95514sols
Code: Select all
+---+---+---+
|125|.7.|...|
|836|...|...|
|749|...|...|
+---+---+---+
|...|123|8..|
|..2|456|...|
|...|789|...|
+---+---+---+
|...|..8|134|
|...|...|287|
|...|...|596|
+---+---+---+
is solved with 4 additional clues

C
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Postby Eioru » Wed Sep 13, 2006 12:04 pm

coloin wrote:Our minimum B159 with 95514sols
Code: Select all
+---+---+---+
|125|.7.|...|
|836|...|...|
|749|...|...|
+---+---+---+
|...|123|8..|
|..2|456|...|
|...|789|...|
+---+---+---+
|...|..8|134|
|...|...|287|
|...|...|596|
+---+---+---+
is solved with 4 additional clues

C


I change its number to
Code: Select all
123.7....
456......
789......
...1254..
..2836...
...749...
.....4158
......247
......396


and on the up&left box can delete number to 7 different kinds
{1,2,7} {2,3,7} {2,6} {2,9} {4} {5} {7,8}
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Postby JPF » Thu Sep 14, 2006 9:04 pm

This B1B5B9 has N solutions (N>=95514)
Code: Select all
 9 5 2 | . . . | . . .
 8 6 3 | . . . | . . .
 7 4 1 | . . . | . . .
-------+-------+-------
 . . . | 9 1 8 | . . .
 . . . | 5 4 2 | . . .
 . . . | 7 3 6 | . . .
-------+-------+-------
 . . . | . . . | 8 2 7
 . . . | . . . | 3 1 4
 . . . | . . . | 9 5 6


is solved with 3 additional clues :

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

JPF
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Postby gsf » Thu Sep 14, 2006 9:53 pm

JPF wrote:This B1B5B9 has N solutions (N>=95514)

N=111559
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Postby JPF » Fri Sep 15, 2006 6:37 am

Thanks gsf.
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a wider slash

Postby claudiarabia » Fri Sep 15, 2006 11:14 pm

Eioru"][quote="coloin wrote:Our minimum B159 with 95514sols
Code: Select all
+---+---+---+
|125|.7.|...|
|836|...|...|
|749|...|...|
+---+---+---+
|...|123|8..|
|..2|456|...|
|...|789|...|
+---+---+---+
|...|..8|134|
|...|...|287|
|...|...|596|
+---+---+---+
is solved with 4 additional clues


If one can reach this with 4 additional clues, JPF's slash pattern is a much straighter example for this. There may be some slash-sudokus in which one can eliminate one clue to reach the JPF-posting previously:

Code: Select all
 . . . . . . . 9 7
 . . . . . . 2 6 1
 . . . . . 3 4 8 .
 . . . . 3 4 5 . .
 . . . 6 2 8 . . .
 . . 6 1 9 . . . .
 . 9 7 2 . . . . .
 8 6 2 . . . . . .
 4 3 . . . . . . .


Claudia
Last edited by claudiarabia on Fri Sep 15, 2006 7:19 pm, edited 1 time in total.
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to many empty rows and columns

Postby claudiarabia » Fri Sep 15, 2006 11:28 pm

Eioru wrote:How about this pattern?

Code: Select all
*.*.*.*.*
.........
*.*.*.*.*
.........
*.*...*.*
.........
*.*.*.*.*
.........
*.*.*.*.*

24-clue
there are 8 empty rows and 1 empty box


It is always a problem if you create sudokus with to many empty rows and columns. I don't know the minimum of rows resp. columns to be filled with at least one seed, but this here is definitely to empty.

The Non-adjacent-clue-thread is a good example for a minimal filled grid in this regard, I suppose.

[url=http://forum.enjoysudoku.com/viewtopic.php?t=4201[url]]http://forum.enjoysudoku.com/viewtopic.php?t=4201[url][/url]

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Re: to many empty rows and columns

Postby m_b_metcalf » Sat Sep 16, 2006 2:22 pm

claudiarabia wrote:
Eioru wrote:How about this pattern?

Code: Select all
*.*.*.*.*
.........
*.*.*.*.*
.........
*.*...*.*
.........
*.*.*.*.*
.........
*.*.*.*.*

24-clue
there are 8 empty rows and 1 empty box


It is always a problem if you create sudokus with too many empty rows and columns. I don't know the minimum of rows resp. columns to be filled with at least one seed, but this here is definitely too empty.


Correct. Rows 4 and 6 are empty, and you can't generate from a template in which two rows (or columns) in the same chute are empty.

Regards,

Mike Metcalf
User avatar
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Postby JPF » Sat Sep 16, 2006 4:54 pm

Code: Select all
*.*.*.*.*
.........
*.*.*.*.*
.........
*.*...*.*
.........
*.*.*.*.*
.........
*.*.*.*.*

m_b_metcalf wrote:Correct. Rows 4 and 6 are empty, and you can't generate from a template in which two rows (or columns) in the same chute are empty.

Yes, this pattern can't have a valid puzzle as daj already pointed it out above.

claudiarabia wrote:It is always a problem if you create sudokus with to many empty rows and columns. I don't know the minimum of rows resp. columns to be filled with at least one seed, but this here is definitely to empty.

To get an answer to your question have also a look at this thread.

JPF
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Re: a wider slash

Postby JPF » Sat Sep 16, 2006 11:13 pm

claudiarabia wrote:
coloin wrote:Our minimum B159 with 95514sols
Code: Select all
+---+---+---+
|125|.7.|...|
|836|...|...|
|749|...|...|
+---+---+---+
|...|123|8..|
|..2|456|...|
|...|789|...|
+---+---+---+
|...|..8|134|
|...|...|287|
|...|...|596|
+---+---+---+
is solved with 4 additional clues

If one can reach this with 4 additional clues, JPF's slash pattern is a much straighter example for this. There may be some slash-sudokus in which one can eliminate one clue to reach the JPF-posting previously


There is no valid slash-puzzle compatible with the minimum B1B5B9 found by coloin :
Code: Select all
 1 2 . . . . . . .
 8 3 6 . . . . . .
 . 4 9 x . . . . .
 . . x 1 2 . . . .
 . . . 4 5 6 . . .
 . . . . 8 9 x . .
 . . . . . x 1 3 .
 . . . . . . 2 8 7
 . . . . . . . 9 6

JPF
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Postby coloin » Tue Sep 19, 2006 12:42 pm

On analysying JPF's puzzle - the B159 with 3 additional clues - see below

I was impressed by the existance of the grid [I couldnt believe it was possible] and wondered how it was produced - I cant believe it was produced by random methods either !

How did he pick the B159 ? [main question]
How did he pick the whole grid fom the 111559 grid solutions ? [long winded but possible to try them all !]
Adding 3 clues is fairly easy !

But on thinking about it...
The information that you need is that the solutions of B145789 is either 0 or more than 1 [ie cant be done]

But it is possible to solve it with a single clue in certain 3-box [e.g B236 in this case] arrangements of 27 cells.

This is not needed with the 4 clue [which are relatively common] that I posted.......but with 3 clues - JPF's brilliant example -

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


Boxes B238 B278 and B236 are solved with a single clue in each of these 3-box combinations.

I realise there is more than 1 way to fill up these 3 box combinations !
JPF wrote:can only have 0 or k solutions ; k=2,3,4,...,27,28*

If it has 2 solutions then the unavoidable sets within the 27 clues can be solved with a single clue in 1,2,3,4.... 6.... 12 ........and 27 ? ways


Suffice to say I think its an impossible ask to solve in 2 clues.....there would be need to be 6 3-box combinations. Each of the 2 clues would
need to simultaneously solve 3 of the 6 combinations.

Well here the 2 at r8c5 solves the 3 relevant 3-box combos
Code: Select all
+---+---+---+
|952|...|...|
|863|...|...|
|741|...|...|
+---+---+---+
|...|546|...|
|...|938|5..|
|...|712|.43|
+---+---+---+
|...|...|872|
|...|.2.|314|
|...|...|956|
+---+---+---+

But I couldnt get less than 3 clues in B6

I dont think it will happen even in sudoku !

C
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Postby JPF » Wed Sep 20, 2006 8:02 pm

coloin wrote:How did he pick the B159 ? [main question]

starting from your minimum B159 + 4 clues ...
the permutations :
col 2,3
col 5,6
row 7,8
col 7,8
give this equivalent puzzle :

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


I removed r1c6=7 and got a 168 solutions puzzle.
I have a program playing with the numbers in the cells to try to find a valid puzzle from a n-solutions puzzle when n is not too large.
Note that the puzzle I ended with, has the same B9 and 6 cells are the same in B1.

coloin wrote:How did he pick the whole grid fom the 111559 grid solutions ? [long winded but possible to try them all !]

It was the consequence of the new B'1B'5B9.

coloin wrote:.......but with 3 clues - JPF's brilliant example -

Thanks !

JPF
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Postby JPF » Sat Sep 30, 2006 11:13 pm

Entertainment :

(can you prove that)

This puzzle :

Code: Select all
 
 . x x | . x x | x x .
 x x x | x x x | . x x
 x x . | x x . | x x x
-------+-------+-------
 . x x | . . . | . x x
 x . x | . . . | x x .
 x x x | . . . | x x x
-------+-------+-------
 x x . | x x x | x x .
 x . x | x x . | x x x
 x x . | x x x | x . x



can only have 0 or 1 solution.

JPF
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Postby Red Ed » Sun Oct 01, 2006 5:56 am

Yes, it's just a long chain of naked singles.
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Postby udosuk » Sun Oct 01, 2006 8:38 am

Red Ed wrote:Yes, it's just a long chain of naked singles.

r8c6-r8c2-r5c2-r4c1-r1c1-r3c3-r3c6-r1c4-r1c9-r2c7-r4c7-r5c9-r7c9-r9c8-r9c3-r7c3
Then it's a matter of proving an empty box is determined by 8 filled box...
(E.g. there is no possible deadly pattern left...)
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