Sudoku- 15 seeds found?

[Rudy Toody]

I was playing with Sudoku logic in Mathematica trying to create a 16 seed grid, which I found. But with later review, I found one seed to be redundant.

I have solved this pattern, but I would like to know if others can do it.

I have a link to the form here.

I have not included the solution so you won't be influenced.

According to existing Sudoku knowledge, the smallest known seed number is 17.

So, I need someone to solve it so I can write it up and get all the glory.

 

[kpb]

I can't solve a single square to get started. I tried it out in a couple web sudoku solvers and they didn't seem to have any luck either.

 

[Rudy Toody]

Originally posted by: kpb
I can't solve a single square to get started. I tried it out in a couple web sudoku solvers and they didn't seem to have any luck either.

Thanks for the effort.

I can solve it using sets with intersection to find if a set matches and complement to remove the found value from all the sets involved with that position.

The sets I use are:

9 row sets
3 tuple sets per row (27)
9 column sets
3 tuple sets per column (27)
2 diagonal sets
3 diagonal tuple sets per diagonal (6)
1 set of column tuples found
1 set of row tuples found

82 sets total.

Each set is initialized to all nine digits.***

I haven't found a solver that is sophisticated enough to solve this. However, people can.

PS: ***Except the found sets which start out empty.

 

[sciencewhiz]

The solver I use says there are multiple solutions, but can't solve it. That may just be because there are less then 17 however. I'm not really sure.

The upper middle set wouldn't happen to have a very easy pattern, does it?

 

[silverpig]

Are you sure it's unique?

 

[gorobei]

the top center set has two sets of alternate pairs. The 9 and 3 can switch places, and the 5 and 7 can swap places. without any other information/seeds there aren't any constraints to eliminate any of the 4 possible arrangements. So it may be possible to have multiple solutions. No prize.

 

[PowerEngineer]

Originally posted by: silverpig
Are you sure it's unique?

This is the pertient question.

Although you certainly could set up a 15-seed grid that had no valid solution, it's much more likely that your grid has more than one valid solution. What you need to show in order to "get all the glory" is that your grid has one -- and only one -- valid solution.

 

[Rudy Toody]

Thanks for the great input, Guys!

This is my first project to learn Mathematica 6.0 and I thought working with unordered sets would be a good challenge. It is. I'm grinning while coding.

Somehow, I missed the 5 - 7 swap. The 3-9 is OK because the other corner always has a 6.

--Fred

 

[Rudy Toody]

Originally posted by: sciencewhiz
The solver I use says there are multiple solutions, but can't solve it. That may just be because there are less then 17 however. I'm not really sure.

The upper middle set wouldn't happen to have a very easy pattern, does it?

This was constructed so the middle 3 columns are completely solved before you solve the outer columns.

--Fred

 

[Rudy Toody]

What had happened is I loaded a non-unique 9x9 to do my mapping on. But I get the same error with a unique grid.

Here is the new blank.
Here is the new solution.

--Fred

 

[sciencewhiz]

Here is an alternate solution to your new blank:

127456983
894123567
356789142
439615728
718342695
265978314
571264839
982531476
643897251

 

[Rudy Toody]

Hi, Guys--

Thanks again for the feedback. The alternate solution posted by sciencewhiz was exactly what I needed.

I did not show the rules for solution because, since I just started working on the puzzles, I was curious what pattern recognition techniques might be used by other solvers.

The new 15Blank and 15Solution each have the rules at the top. The 14Solution uses the identical set of rules.

I am hoping someone can find an alternate solution when following the rules.

If no alternate can be found or shown to exist, then we need to determine if this is truly a lower seed or the rules get in the way by forcing the solution.

--Fred


I got interested in the puzzles when I started crunching Project Sudoku for TeAm AnandTech. Try it!

 

[PowerEngineer]

Hey Rudy,

I'm pretty sure a sudoku square with more than a single solution (that is consistent with the starting seeds) will not be solvable in the sense that you can work your way through the square always finding unique values for each open value until it is complete.

Your latest 15Solution shows the following entries in the three middle rows of the right three columns:

456
645
564

It seems to me that you also get valid solutions when you rotate these to:

564
456
645

or

645
564
456

Actually, I think the same is true for the 4-5-6 entries in the bottom rows of the left column as well.

 

[Rudy Toody]

Originally posted by: PowerEngineer
Hey Rudy,

I'm pretty sure a sudoku square with more than a single solution (that is consistent with the starting seeds) will not be solvable in the sense that you can work your way through the square always finding unique values for each open value until it is complete.

Your latest 15Solution shows the following entries in the three middle rows of the right three columns:

456
645
564

It seems to me that you also get valid solutions when you rotate these to:

564
456
645

or

645
564
456

Actually, I think the same is true for the 4-5-6 entries in the bottom rows of the left column as well.

You are correct about rotating the 4-5-6 in either or both outer sets, however to keep the requirement that the diagonal tuples be consistent you would need to rotate those rows in the middle set as well. The top line middle column seeds 4-5 prevent that rotation.

Thanks.

--Fred

 

[Rudy Toody]

PowerEngineer, I see what you mean now. The diagonal rule is something the creator needs to do during mapping, and if we want to give that information to the solver, then we must include 2 more pieces of information, thus making this a 17 seed puzzle.

I'm going back to the drawing board. Thanks for your feedback everyone.

--Fred

 

[Howard]

Seeds? What?

 

[silverpig]

Originally posted by: Howard
Seeds? What?

Numbers you're given to start with.

 

[Howard]

So are we trying to find a solvable puzzle which gives the minimum # of starting numbers?

 

[FallenHero]

Originally posted by: Howard
So are we trying to find a solvable puzzle which gives the minimum # of starting numbers?

that doesnt have more than one solution

 

[Triumph]

link to 17 seed puzzle please, i want to try it.