The New Sudoku Players' Forum

[Papy]

Do you that Papy is creasy?

Just like St Thomas he bekleive only what he sees.

So on the net you find the number of latin squares with the sudoku specifications But no where you find the method uses. Mathématiciens keep the secret of the calculation
Papy is not a mathématicien only a hard coder! with a personnal computer
E650 processior. No Cray or Bue Gene. Only a computer made by his son.

So if yo don't find the way to compute he total the only solution is to generate them.

But with a personnal it was a dream... before

After analising the Gordon Collection (Thanks to him) anda long treap into the proceessor I code a method to generate thm
Perhaps 100 application before the good

When ou want to compute the number of latin squares you compute a specific disposition, after you compute the number of specific configurations and to finish you mutiply the two numbers


The specific value is when you fixe one row and one column to a specifc
value . It's the mnimum of cues that you need to foind a solution: on the sudoku the number is 17 : it's wll the smaller number of clues of a Sudoku
grid.

But for the sudoku grid the nmber is not the number of Latin Squares It less because a Soduko grid is a Latin square 9*9 but with specifics contraints: boxes

And no one know how to compute the number of variations with a grid. On 'normal latin square' you multiply by !n and after !n-1
In facty it easy to compute . Then the number is !n*72


An other problem is to compute the number of squares for a specific disposition. Te numbe find on the web id very important

4 pour 4*4
56 pour 5*5
9 408 pour 6*6
16 942 080 pour 7*7
535 281 401 856 pour 8*8
377 597 570 964 258 816 pour 9*9
7 580 721 483 160 132 811 489 280 pour 10*10


How to compute 377 597 570 964 258 816 ?and verify it?
In fact I find a way to separate this nimber in 82944 sub-classe

I compute all the 82944 classes( one week oàn pmy personnal computer) and add all them

I have the intermediats calculation to veridfy them.
The results is only..

1 091 381 429 324
* 72
78 579 462 911 328
* 362880(!9)
==================
28 514 915 501 262 704 640


Every one can compute it again verify it and find an error.
But I can say today: I can compute 28 514 915 501 262 704 640 latin squares Sudoku 9*9 and say that my method compute all the square possibles and tjhhis number is 2.8e23

Until you find a new number
If you want etails ask me but they do not interest the player only coder (and Coloin)

I work on a book.

Papy