The New Sudoku Players' Forum

by **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

by **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.

by **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

by **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).

by **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

by **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

by **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: ....*.... .*....*.. *.*...*.* ...*.*... ....*.... .*......* .*.....*. *...*.... ...*.*... ......*.* .*.....*. ..*.*.... ....*.... ...*...*. *.*...*.* *.*...... ....*.... .....*.*.

by **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 | +-------+-------+-------+

by **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

by **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 | +-------+-------+-------+

by **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

by **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 | +-------+-------+-------+

by **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

by **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.

by **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

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