What will I get if I count all solutions of this grid?

evert · Posted: Mon Mar 13, 2006 2:30 pm Post subject:

It occurs to me that renumbering is also a transformation that keeps a grid "equivalent".
You might want to read this description of operations:
http://www.csse.uwa.edu.au/~gordon/sudokumin.php

I don't understand your question completely - you might use some terms differently from what I'm used to.

What's a field exactly?

treffer · Posted: Mon Mar 13, 2006 3:04 pm Post subject:

I was looking for a setup of a field that eliminates rotations or similar solutions of two sudokus.

If you have two solutions of the posted field they will always be different in a way that

won't allow you to make them match. (stolen from your link)

BUT:
I am not aware what happens if you allow "Permutations of the 9 symbols".
I do not know if any sudoku can be rearranged in a way that its solution will match the above field. (Or the other way round: can any get ALL possible sudokus if I use the solutions of this field)
OR:
Can I generate a Partition of a Set (Wikipedia)

Any hints/proves etc. on that would be nice.

evert · Posted: Mon Mar 13, 2006 4:39 pm Post subject:

I understand the question now.

evert · Posted: Wed Mar 15, 2006 10:17 pm Post subject:

If I take a filled grid and in that grid I can find
9 different numbers positioned in
9 different rows and
9 different columns and
9 different boxes,
then I assume that the grid can be rearranged in such a way that its solution will match the above field.

I have no idea how to prove this.

I wrote a recursive program that looks for 9 such cells in a particular grid.
Out of 10 arbitrary grids all 10 of them contained such a series of 9 cells.

coloin · Posted: Fri Mar 31, 2006 6:43 pm Post subject:

I think every grid will have at least one instance of this general pattern - ....some essentailly different grid types will have more. Red Ed is the expert here.
http://www.afjarvis.staff.shef.ac.uk/sudoku/sudgroup.html

I think an approximation to the number of grid solutions with this specific pattern - ie [as posted] will be will be Bertrands number[6*10^21] devided by 9^9. Each clue reduces independantly the number of solutions by 9.

I think the general pattern of every different clue number in its own row and column may well be found somwhere in every grid. Can you find one which doesnt have this ?

The relevance to me......well it might help [not sure how] in finding the largest minimal sudoku puzzle.
Currently stands at 35,
http://www.sudoku.com/forums/viewtopic.php?t=1448&start=45
contributions welcome.

Why not post it as a new thread http://www.sudoku.com/forums/viewforum.php?f=4 there ?

C

treffer · Posted: Wed Apr 05, 2006 8:43 pm Post subject: The answer....

&#%$!

and suddenly the answer appears...

Currently I have a collection of 36628 distinct Sudoku configurations with 17 entries

this means that he has 36628 distinct Sudoku configurations, that won't match each other using the above transformations... I was dull, sorry for wasting your time.

I can't escape from one of these 36628 Sudokus, leading to at least 36627 different sudocu classes I can't generate....

sorry guys...

[edit]
Forgotten to quote:
http://www.csse.uwa.edu.au/~gordon/sudokumin.php: Currently I have a collection of 36628 distinct Sudoku configurations with 17 entries

evert · Posted: Wed Apr 05, 2006 9:16 pm Post subject:

Am I right that you mean that one or more of these 17 clue sudokus can NOT be rearranged
such that its solution will match the grid from your first post - allowing permutation
of the 9 symbols?

Can you mention that particular grid? I'd like to check if my program indeed does NOT find 9 different numbers
positioned in 9 different rows/columns/boxes.

treffer · Posted: Wed Apr 05, 2006 9:23 pm Post subject:

Sorry, just wrong thinking... The solutions i start with are different... Sorry... That's the point... I'm going mad, sorry again Sad

coloin · Posted: Wed Apr 12, 2006 12:57 pm Post subject:

No I dont think you are wrong !

It is the whole solution grid which will have "your pattern " somewhere in it - you cant just look at the puzzle clues.

C

Papy · Posted: Thu Aug 17, 2006 11:10 am Post subject: @treffer

Hi,
About symbol permutation you can invert them the grid will always be the same and good. use letters no nuimbers: the reslt is the same:
If you invert all the 1 in 2 the 2 in 3 a,nd the 32 in on the grid is always the same.

About the 36000 17 clues collection. It's theGordon file?
Becxause in fact you have 'only' 1000 distincts grids and
17 clues dispositions
For me the others 35000 grids are only permutation!
I write him to know how he determine thart a grid is 'original'
If some one know metods I'm interested
I'm also inerressing for method to revert a permuted grid!
(I can dream sometime Confused

)

coloin

This subject is coming up again.....

I think the answer might be 6*10^21/9^9

To repeat

I think the general pattern of every different clue number in its own row and column may well be found somwhere in every solution grid. Can you find one which doesnt have this ? In which case the answer might well be 6*10^21 / 9!

I think this pattern comes up in some puzzles - but usually not the complete 9. This might be what was confusing treffer

Every valid puzzles looks to have at least 5 of this "inverse rookery pattern"

Many have 7 and some have the complete set of 9

Comments please

C