I'm claiming it's possible to write Sudoku solvers that have some constant upper bound on execution time. If you read this as "a short amount of time", you are misreading it.
I'm also not saying that this is true for all Sudoku solvers, since you could write one that sometimes just decides to uselessly burn cycles for a few centuries before returning a correct solution.
Here's that simple argument again: Sudoku can be solved in time at most exponential in the input size. The input size of 9x9 Sudoku is constant. The exponential of that constant is a constant. Not a very interesting argument? I agree, so I'm dropping this now.
I'm also not saying that this is true for all Sudoku solvers, since you could write one that sometimes just decides to uselessly burn cycles for a few centuries before returning a correct solution.
Here's that simple argument again: Sudoku can be solved in time at most exponential in the input size. The input size of 9x9 Sudoku is constant. The exponential of that constant is a constant. Not a very interesting argument? I agree, so I'm dropping this now.