  Let P be a permutation expressed as a product of nontrivial disjoint cycles.
When writing P as a product of distinct transpositions none equal to a factor
of P, what is the smallest number of transpositions that can be used? We answer
this question and give applications to mind-switching problems that have arisen
in connection with the popular sci-fi television series Futurama and Stargate
SG-1.
