I tried asking this on StackOverflow and it was quickly closed for being too broad, so I come here to get the mathematical part nailed down, and then I can do the rest with no help, most likely.
From this web page, I learned that there are 5,472,730,538 essentially different solved sudoku grids.
Please, I beg you, do not respond unless you have read the entire webpage and have a decent understanding of it. You can think of a 9x9 sudoku as being represented by a string of 81 numbers, separated by commas.
I want to find a way to generate one sudoku board from each of the 5,472,730,538 groups, do some quick analysis on it, and move on to the next board, continuing until all 5.4 billion are analyzed. In this way, I will have analyzed all possible essentially different Sudoku boards. I am not familiar with GAP.
So, I need someone, if they are willing, to help me bridge the knowledge gap I have, which is this: How do I go from this web page to actually finding (iterating through) each solution?
I do not expect a full detailed thorough answer on this. Instead, any post that I think is helpful to me in reaching my goal will be upvoted, no matter how short or how detailed.
Thanks to Nick Gill's suggestion, I contacted Frazer Jarvis himself and here is his very helpful reply:
The method we used simply evaluated the number of puzzles there had to be, and didn't count them by listing them all, so it wasn't a constructive proof in that sense. Nor can the proof be made to give a list, as far as I can see. As you are probably aware, this work of mine dates to 2005, and my active interest in Sudoku and related mathematical problems probably ended soon after, although I followed forums for a little while (my wife still likes doing them, but it has been a long time since I did one!) - but I did read towards the end of that time that someone had made a file of all of these. I don't remember who it was, however. You may be able to find the forum postings if you look around the internet. I'll have a quick look around too.
OK - the forum that contained the discussions no longer exists, but has been retitled, and is now at http://forum.enjoysudoku.com/sudoku-the-puzzle-f5.html
Ah - here's the thread: http://forum.enjoysudoku.com/catalog-of-all-essentially-different-grids-t6679.html - perhaps you could contact someone there?
Best wishes, Frazer
He also added later:
For what it's worth, the discussions about the number of different grids is in the thread http://forum.enjoysudoku.com/su-doku-s-maths-t44.html