Transformation

rallveird · Posted: Thu Jun 16, 2005 6:33 am Post subject: Transformation

I was reading upsidedownface post in http://www.setbb.com/phpbb/viewtopic.php?t=5&mforum=sudoku and was wondering how many transformation you have on a solution.

According to his 5 methods to transform you get:

1. 9! = 362880
2. 3!^3 = 216
3. 3!^3 = 216
4. 3! = 6
5. 3! = 6

If you then combine them you get:

216*216*6*6 = 1679616 different patterns

and

362880*216*216*6*6 = 609499054080 different grids

This will not be entire correct since 2 empty row/grid/boxes will not make any difference if you swap them, and if not all numbers from 1-9 are present in the grid you will not get that amount of grids.

But still, that's a lot of grids which is only a transformation of 1 single startgrid.

And if you divide the number of possible grids 6670903752021072936960 with the transformation grids you get 10944895988.

Hm, I have to find out how many real starting grids you got for a spesific starting number. Will there be more than 1?

And another though, is it possible to find logic methods which can benefit from transforming the grid first?

Anyone?