Nice.
so, representing the magnetic polarity of the magnets on the end, and the coil in the center, it has to be
+- -......+ -+
to run to the left, or
-+ -......+ +-
to run to the right.
-+ -......+ -+ and +- -......+ +-
won't go anywhere. I'm out on a limb here! But that's got to be right.