Given a Sudoku puzzle with only one right answer is it always possible to solve it without using trail and error?
Not always. There is a practically infinite number of grids that
cannot be solved using even the most advanced techniques, including
some that blur the line between logic and trial and error. A
software and puzzle designer known as Ruud has compiled a list of
50,000 such puzzles, which can be found here:
http://www.sudokuvault.com/top50000.zip Unfortunately, nearly all
sudoku puzzles found in American publications are computer
generated, so there is no guarantee you won't come across puzzles
that cannot be solved logically, but a majority of them still
can.