  This paper presents a systematic method to solve difficult 9 x 9 Sudoku
puzzles by hand. While computer algorithms exist to solve these puzzles, these
algorithms are not good for human's to use because they involve too many steps
and require too much memory. For humans, all one can find in the literature are
individual tricks, which used together in ad hoc ways can be used to solve some
puzzles--but not all. To the author's knowledge, a systematic procedure made up
of well-defined steps that can be carried out by hand and solve all puzzles has
not been devised. This paper proposes one such technique--the "minuet" method.
It is based on a new system of markings and a new way of simplifying the
puzzles that can be easily carried out by hand--or by computer. The author has
solved hundreds of puzzles of the most difficult kind ("evil" in Sudoku's
parlance) and never found one that could not be solved. The average time to
solve one of these puzzles is slightly over 1 hour. It is conjectured that this
method can solve all well-posed 9 x 9 puzzles. The method's distinguishing
feature is a "minuet" strategy that is applied when the puzzle cannot be
further simplified with basic tricks. The strategy consists in concurrently
developing two potential solutions, sometimes alone and sometimes in concert as
if they were dancing a minuet.
