CONTACT M (for mathematics)

You might have guessed that a website designed and developed by a mathematics guy would include some mathematics.

You found it.

It isn't very available, because the abstruse nature of the discussions here is not meant for everyone.

Now to work.

Considering that there are nine ways to fill the upper left square,

eight ways to fill the next square,

seven ways to fill the next square,

six ways to fill the next square,

five ways to fill the next square,

four ways to fill the next square,

three ways to fill the next square,

two ways to fill the next square,

and one way to fill the upper right square,

and there are six, five, six, five, four, three, two, and one ways to fill the squares that make up the leftmost column,

THEN

There is a minimum of 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 x 6 x 5 x 6 x 5 x 4 x 3 x 2 x 1 or 115,339,230,720 minimum different sudoku puzzles. So, don't worry, we won't run out.

Next. Finding out exactly how many different Sudoku puzzles there are is a bit more tricky.

Considering only the constraints of rows, columns, and squares, and including all possibilities otherwise, there are approximately 10³⁰ different solutions. This means only that there are fewer than 10³⁰ different solutions. I just have to work out constraints based on singular solutions and complicated constraints based on complicated stuff. (Notice the careful use of the extremely important mathematical term "stuff".)

I'll get to such things soon. I'll also be working on the minimum hint hypothesis.

All in good time, I guess.