Is it possible to count number of 10X10 sudoku matrices, with 0-9 digits in it.
In terms of constraints, the sum of elements in rows and also in columns have to be fixed, in this case, 45. is this condition enough to count all the possible cases.

The restriction you describe is not the usual sudoku restriction. It sounds like the objects you really are interested in are Latin squares: en.wikipedia.org/wiki/Latin_square
– JBLSep 21 '10 at 13:12

No, that condition isn't enough. Put 0s down the main diagonal, and 5s everywhere else. Most people wouldn't call that a latin square, much less a sudoku.
– Jonah OstroffSep 21 '10 at 13:25

2

Ordinary 9x9 sudoku puzzles have a uniqueness restriction on the 3x3 squares inside, and there doesn't seem to be a meaningful way to make this happen for numbers like 10 that are not squares of integers. I think this question may be worth closing.
– S. Carnahan♦Sep 21 '10 at 14:57

1

Scott, I have little doubt the question is worth closing. But meanwhile, people publish 12 by 12 puzzles where the internal blocks are 3 by 4 rectangles. So for 10 by 10 you could tile with 2 by 5 rectangles for the extra restriction.
– Will JagySep 21 '10 at 19:44