The New Sudoku Players' Forum

[Papy]

After test I give you my conclusions and what I found

You have 362880 ways to sort the 9 digits a row and 5 000 billions of billions the 81
But in fact many of the grids are equal: just isomorph of the Sudoku.
And the valid Latin squares?Are they all isomorphs of any?
For me yes but you have a lot of original:

Just for a bloc you have 2 612 735 of dispositions
How to compute thius number?
It's easy you juste have to genrate bloc latin square with the same first row
At the end you have a set of 2 612 735 blocs.

Now take any bloc you want and renumber the digits (icreating an somorphs) to be in the ordeer you chose the result is necessary in your set of 2 613 000

For example if you choose to renumer the first ROW 123456789
It's still possible: you have always the nine digits.
In Fact the principal interest is that you can use this to solve hardest
sudoku
But silence....Wait for the demonstration
This result is interressing also to create.

Papy

[Red Ed]

Just for a bloc you have 2 612 735 of dispositions
How to compute thius number?
It's easy you juste have to genrate bloc latin square with the same first row
At the end you have a set of 2 612 735 blocs.

You can calculate this number by hand (getting 2612736) as demonstrated by Frazer here.
(btw, small clarification: by "bloc", I assume you mean "chute")

Now take any bloc you want and renumber the digits (icreating an somorphs) to be in the ordeer you chose the result is necessary in your set of 2 613 000

No it isn't. The 2612736 number comes from fixing the order of the digits (in the top row of a band, in Frazer's case). Any renumbering will necessarily give you a chute/"bloc" outside of that set of 2612736.

In Fact the principal interest is that you can use this to solve hardest sudoku

OK, now you're saying something new. Looking forward to seeing the details ...

[Papy]

No it isn't. The 2612736 number comes from fixing the order of the digits (in the top row of a band, in Frazer's case). Any renumbering will necessarily give you a chute/"bloc" outside of that set of 2612736.

yes it's!

Because you can ALWAYS renumber a block (3 boxes h or V) to have
the same first row also the new Latin bloc is always in thre 2612736
(I forget the 0!)

Give mùe a block that we can change the 1 row to 123456789 WITHOUT changing the position of the clues

It's impossible!


Papy

[Red Ed]

Yes, apologies there. The language barrier was to blame. I agree that, with the top row fixed to 123456789 (say), there are only 2612736 possibilities for the rest of the band. This has been well known for nearly two years now.

I wonder where you're going with this. The reduction to 2612736 possibilities is the most obvious thing you can do. But you can go further. Up to isomorphism, there are only 416 possible classes of band. And if you only care about the number of completions of from a filled band to a filled grid (so contents of minicolumns matter, but order doesn't) then there are only 44 configurations that matter. So ... your point is ...?