Ask for some patterns that they don't have puzzles.

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

Postby Havard » Tue Jun 26, 2007 7:38 pm

claudiarabia wrote:I'm still unfamiliar with solving multisolutional sudokus.


And please keep it that way.:) A sudoku with more than one solution is not a sudoku in my opinion. You would just have to arbitrary choose numbers to fill in the grid, no logic or anything involved. Pointless...:)

Havard
Havard
 
Posts: 377
Joined: 25 December 2005

Postby Mauricio » Tue Jun 26, 2007 11:10 pm

"Sudokus" with multiple solutions can be fun too, but not from a human viewpoint

JPF wrote:For the fun , here's one with 1000 solutions:)
Code: Select all
 1 . 2 | . 3 . | 4 . 5
 . 3 . | 6 . 5 | . 1 .
 5 . 7 | . 4 . | 8 . 3
-------+-------+-------
 . . . | . . . | . . .
 . 8 . | . 1 . | . 4 .
 . . . | . . . | . . .
-------+-------+-------
 8 . 4 | . 5 . | 3 . 6
 . 5 . | 4 . 6 | . 7 .
 6 . 1 | . 7 . | 9 . 4



Funnier still, I found this with almost random generation, not exactly random.
Code: Select all
 1 . 2 . 3 . 4 . 5
 . 4 . 1 . 5 . 6 .
 5 . 6 . 2 . 1 . 3
 . . . . . . . . .
 . 6 . . 5 . . 4 .
 . . . . . . . . .
 6 . 5 . 4 . 7 . 1
 . 3 . 5 . 7 . 2 .
 7 . 1 . 6 . 5 . 4             30208 solutions

I am sure more "improvement" (more solutions and the same pattern) can be done using a more intelligent approach.
Mauricio
 
Posts: 1174
Joined: 22 March 2006

Postby JPF » Wed Jun 27, 2007 1:50 pm

Mauricio wrote:Impressive work!, JPF
thanks.
Mauricio wrote:BTW, I tried to create a sudoku with 19 clues or less and horizontal+vertical symmetry, unsuccesfully. Can anyone help me?

I thought the pattern below could be a good candidate...
but the puzzles I found have at least 2 solutions :
Code: Select all
 1 . . . . . . . 2
 . . . 3 . 4 . . .
 . . 4 . . . 5 . .
 . 4 . . . . . 6 .
 7 . . . 2 . . . 8
 . 3 . . . . . 4 .
 . . 1 . . . 3 . .
 . . . 7 . 5 . . .
 9 . . . . . . . 1


Any takers ? or is it a non valid pattern ?

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby ravel » Wed Jun 27, 2007 4:21 pm

The pattern should be valid (though maybe impossible), but after singles only your puzzle ends with a nice 10 cells unique loop:
Code: Select all
 +-------+-------+-------+
 | 1 8 3 | 5 6 9 | 4 7 2 |
 | 5 2 7 | 3 8 4 | 6 1 9 |
 | 6 9 4 |12 7 12| 5 8 3 |
 +-------+-------+-------+
 |28 4 9 |18 3 7 |12 6 5 |
 | 7 1 5 | 4 2 6 | 9 3 8 |
 |28 3 6 | 9 5 18|12 4 7 |
 +-------+-------+-------+
 | 4 7 1 |28 9 28| 3 5 6 |
 | 3 6 2 | 7 1 5 | 8 9 4 |
 | 9 5 8 | 6 4 3 | 7 2 1 |
 +-------+-------+-------+
So this is a sample for a multi solution puzzle, that easily can be solved manually (without guessing).
ravel
 
Posts: 998
Joined: 21 February 2006

Postby JPF » Wed Jun 27, 2007 8:35 pm

Mauricio wrote:Funnier still, I found this with almost random generation, not exactly random.
Code: Select all
 1 . 2 . 3 . 4 . 5
 . 4 . 1 . 5 . 6 .
 5 . 6 . 2 . 1 . 3
 . . . . . . . . .
 . 6 . . 5 . . 4 .
 . . . . . . . . .
 6 . 5 . 4 . 7 . 1
 . 3 . 5 . 7 . 2 .
 7 . 1 . 6 . 5 . 4         30208 solutions

I am sure more "improvement" (more solutions and the same pattern) can be done using a more intelligent approach.

Code: Select all
 1 . 2 | . 3 . | 4 . 5
 . 6 . | 5 . 4 | . 7 .
 4 . 5 | . 1 . | 6 . 8
-------+-------+-------
 . . . | . . . | . . .
 . 5 . | . 4 . | . 8 .
 . . . | . . . | . . .
-------+-------+-------
 6 . 4 | . 7 . | 5 . 9
 . 1 . | 4 . 5 | . 6 .
 5 . 7 | . 6 . | 8 . 4          50112 solutions


more solutions, but not an intelligent approach...
I wonder what is the max.

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby JPF » Fri Jun 29, 2007 12:48 pm

This 19 clues-pattern is not too tough to match :

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


JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby Eioru » Mon Jul 02, 2007 5:13 pm

Some 18-clue pattern,

Code: Select all
AAABBBAAA   AAABBBCCC
AAABBBAAA   AAABBBCCC
AAABBBAAA   AAABBBCCC
BBBAAABBB   CCCAAABBB
BBBAAABBB   CCCAAABBB
BBBAAABBB   CCCAAABBB
AAABBBAAA   BBBCCCAAA
AAABBBAAA   BBBCCCAAA
AAABBBAAA   BBBCCCAAA


while A,B,C has 2 clues.
For example:
Code: Select all
....*....   .*....*..
*.*...*.*   ...*.*...
....*....   .*......*
.*.....*.   *...*....
...*.*...   ......*.*
.*.....*.   ..*.*....
....*....   ...*...*.
*.*...*.*   *.*......
....*....   .....*.*.
Eioru
 
Posts: 182
Joined: 16 August 2006

Postby Mauricio » Tue Jul 31, 2007 8:25 am

I would be happy and surprised if anyone can tackle these patterns
Code: Select all
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . 1 |
| . . . | . . . | x x x |
+-------+-------+-------+
| 1 2 3 | x x x | x x x |
| 4 5 6 | 1 x x | x x x |
| 7 8 9 | x x x | 1 x x |
+-------+-------+-------+
| x 1 x | x x x | x x x |
| x x x | x 1 x | x x x |
| x x x | x x x | x 1 x |
+-------+-------+-------+

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

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

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

+-------+-------+-------+
| . 1 . | . . . | . . . |
| . . . | . . 1 | . . 2 |
| . . . | . . . | . . 1 |
+-------+-------+-------+
| . . 1 | . . 2 | . . . |
| x x x | 1 x x | x x 3 |
| x x x | x x x | 1 x 4 |
+-------+-------+-------+
| 1 x x | x x x | x x 5 |
| x x x | x 1 x | x x 6 |
| x x x | x x x | x 1 7 |
+-------+-------+-------+
Mauricio
 
Posts: 1174
Joined: 22 March 2006

Postby JPF » Tue Jul 31, 2007 4:08 pm

I think one can extend your first pattern to this one :

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 | x x x |
+-------+-------+-------+

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby Mauricio » Tue Jul 31, 2007 4:33 pm

JPF wrote:I think one can extend your first pattern to this one :

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 | x x x |
+-------+-------+-------+

JPF

Of course, if there is a puzzle with the above pattern, then r1c9 is redundant, so there is a puzzle with my fisrst pattern. The same thing can be done to my 3rd and 4th pattern, so they can be entended to:
Code: Select all
+-------+-------+-------+
| . . . | . . . | . . 9 |
| . . . | . . . | . . 1 |
| . . . | . . 1 | . . 2 |
+-------+-------+-------+
| . . . | x x x | x x 3 |
| 3 x x | x x x | x x 4 |
| x x x | x x x | x x 5 |
+-------+-------+-------+
| x x x | 1 x x | x x 6 |
| x x x | x x x | 1 x 7 |
| x x x | x x x | x x 8 |
+-------+-------+-------+

+-------+-------+-------+
| . 1 . | . . . | . . 9 |
| . . . | . . 1 | . . 2 |
| . . . | . . . | . . 1 |
+-------+-------+-------+
| . . 1 | . . . | x x 3 |
| x x x | 1 x x | x x 4 |
| x x x | x x x | 1 x 5 |
+-------+-------+-------+
| 1 x x | x x x | x x 6 |
| x x x | x 1 x | x x 7 |
| x x x | x x x | x 1 8 |
+-------+-------+-------+
Mauricio
 
Posts: 1174
Joined: 22 March 2006

Postby JPF » Tue Jul 31, 2007 5:06 pm

I agree:)
but i'm not sure I understand why you put digits in some patterns.
What about the pattern 3 for example and this possible generalization :

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 |
+-------+-------+-------+


The best I got (with a few grids though) is 3 solutions.

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby Mauricio » Tue Jul 31, 2007 5:37 pm

JPF wrote:but i'm not sure I understand why you put digits in some patterns.

Oh.
Digits given are fixed cells, ie, you may generate a sudoku with that patterns AND the digits given must be kept the same.

JPF wrote:
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 |
+-------+-------+-------+

The best I got (with a few grids though) is 3 solutions.

Code: Select all
2 solutions
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . 1 |
| . . . | . . 1 | . . 2 |
+-------+-------+-------+
| . . . | 1 2 3 | 4 5 6 |
| 1 2 4 | 7 6 5 | 8 3 9 |
| 3 5 6 | 4 9 8 | 1 2 7 |
+-------+-------+-------+
| 2 4 8 | 3 1 7 | 6 9 5 |
| 5 6 7 | 8 4 9 | 2 1 3 |
| 9 1 3 | 6 5 2 | 7 4 8 |
+-------+-------+-------+
Mauricio
 
Posts: 1174
Joined: 22 March 2006

Postby JPF » Wed Aug 01, 2007 7:27 am

Mauricio,
Nice find again.

Your puzzle is equivalent to :
Code: Select all
 . . . | . . . | . . .
 . . . | . . . | . . 1
 . . . | . . 1 | . . 2
-------+-------+-------
 . . . | 2 1 7 | 6 9 3
 1 2 9 | 3 5 6 | 7 8 4
 7 6 3 | 4 9 8 | 2 1 5
-------+-------+-------
 2 9 8 | 1 7 5 | 4 3 6
 6 3 5 | 9 8 4 | 1 2 7
 4 1 7 | 6 3 2 | 9 5 8

It doesn't prove that your pattern 3 is not valid (r5c1=1)

I think that my statement is stronger,:) , i.e. :

Pattern 3 JPF non valid ==> Pattern 3 Mauricio non valid.
Am I right ?

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

Postby Mauricio » Wed Aug 01, 2007 7:35 am

JPF wrote:Pattern 3 JPF non valid ==> Pattern 3 Mauricio non valid.
Am I right ?

I'd think so, but just to clarify matters, can you post Patter 3 JPF and Pattern 3 Mauricio?

Shortly I will be posting a new topic that has relations to the patterns I posted.
Mauricio
 
Posts: 1174
Joined: 22 March 2006

Postby JPF » Wed Aug 01, 2007 7:48 am

Code: Select all
Pattern 3 JPF
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . 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 |
+-------+-------+-------+

Pattern 3 Mauricio
+-------+-------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . 1 |
| . . . | . . 1 | . . 2 |
+-------+-------+-------+
| . . . | x x x | x x 3 |
| 3 x x | x x x | x x 4 |
| x x x | x x x | x x 5 |
+-------+-------+-------+
| x x x | 1 x x | x x 6 |
| x x x | x x x | 1 x 7 |
| x x x | x x x | x x 8 |
+-------+-------+-------+

JPF
JPF
2017 Supporter
 
Posts: 3752
Joined: 06 December 2005
Location: Paris, France

PreviousNext

Return to General