I have to prove that if you put some random number (between 1 and 9) at any of the fields of an empty Sudoku, it is always solvable, but I do not find the way to it.
One way to prove it would be solving the 9*81 possible initial values, but doesn't seem like a proper way to proceed.
I also did think about formulating the problem as an equation system and prove that it has many solutions, but I'm not sure how to do this.
Any idea out there?
Thanks.