minimum number of clues for sudoku 6*6

xcormier

I am french,and I found a sudoku 6*6 with exactly 8 clues which has an unique solution :

040 003
000 060

000 004
006 002

030 010
000 000

I wonder if an other person has found less clues than me.
but we can see that the minimum number of clues for a 6*6 is inferior or egal to 8.

NB: I have made an application for generating and solving sudokus on a mathematic application called MAPLE.
maplesoft->application center->Mathematics->General->maplet de sudoku version 4.(xavier cormier).

Pat · Posted: Sun Mar 07, 2010 12:55 pm Post subject:

Pat · Posted: Tue Mar 09, 2010 9:54 am Post subject: 2x4

2x3

2x4

xcormier · Posted: Tue Mar 09, 2010 10:45 am Post subject: sudoku 4x2 with 18 clues

I have found with my program several (minimum) sudokus 4*2 with 18 clues.
here is an example:

0000 6000
0208 0040

4000 0051
7060 0020

0301 0070
0070 0000

8003 0000
0000 0402

Afmob · Posted: Tue Mar 09, 2010 11:30 am Post subject:

Here is a symmetric 2x4 Sudoku with 14 clues:

1 2 3 0 0 0 0 0
0 0 0 0 0 0 4 0
5 0 0 6 0 0 0 0
0 0 0 0 0 0 0 3
6 0 0 0 0 0 0 0
0 0 0 0 3 0 0 2
0 7 0 0 0 0 0 0
0 0 0 0 0 6 5 8

Running my programm through all possible 2x4 Sudokus with only 11 clues, I was able to prove that the true minimum is either 12,13 or 14. I haven't found one with 12 or 13 clues so far.

Pat · Posted: Tue Mar 09, 2010 11:39 am Post subject:

Afmob · Posted: Tue Mar 09, 2010 12:12 pm Post subject:

I found it while going through all symmetric 14 Clues 2x4 Sudokus after about 100 hours. Going through all 12 Clues would take roughly 1,5 years and all 13 Clues 20 years, so it's kind of doable. Very Happy

By the way, there is no rotational symmetric 12 Clues 2x4 Sudokus (search took about 200 hours).

Pat · Posted: Sun Mar 14, 2010 12:14 pm Post subject: re: 2x4

Afmob

Afmob · Posted: Sun Mar 14, 2010 2:26 pm Post subject:

I probably hid for too long. Laughing

I stopped looking for 14 clues Sudokus after I found this symmetric one. But after some rewrites of my programs and using a new canonical form (similar to but not the same as the popular minlex form) I found another one with 14 clues.

pseudo coup · Posted: Sun Mar 21, 2010 7:51 am Post subject: re: 2x4

Your first puzzle
is even prettier if we swap 57

Pat · Posted: Sun Mar 28, 2010 1:10 pm Post subject:

123...........4.7..6...........36...........3..2.5...........678

Code:

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

..12..........3.4......5...16......78...3......45...........21..

Code:

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

Pat · Posted: Sun Mar 28, 2010 1:15 pm Post subject:

Afmob · Posted: Sun Mar 28, 2010 1:41 pm Post subject:

I didn't want to make a new post because I thought it wasn't important enough since I had even found 13 Clues 2x4 Sudokus with less solutions (15 or 17, if I remember correctly) but I didn't keep them.

Concerning you're question: Add R4C6 = 7

Pat · Posted: Fri Apr 02, 2010 6:50 am Post subject:

Afmob wrote:

I thought it wasn't important enough
since I had even found 13-Clues 2x4 Sudokus with less solutions
(15 or 17, if I remember correctly)
but I didn't keep them.

Afmob · Posted: Fri Apr 02, 2010 8:59 am Post subject:

That's impressive! I'll only look for 13 clue Sudokus with few solutions for fun since it doesn't seem to help finding one with a unique solution.

Of course, my main program stops when it finds a second possible solution for a puzzle. Otherwise it would take too long going through all possible Sudokus.