He can't win. Permutations also have a parity which is changed by a transposition . A transposition is a permutation which exchanges the place of two objects whilst leaving all the other objects unmoved. An important fact is that any permutation on n objects can be done with a series of transpositions. It is a further fact that if it can be done in an even number of permutations then it can't be done in an odd number and vice versa.
Every permutation is equivalent to a product of transpositions.
A simple way to see this is to think of how you might reorder a dozen eggs in an egg carton. Suppose the eggs were numbered 1 to 12. If you were given a permutation of the eggs and told to rearrange the eggs into that permutation you might begin with the first place in the egg carton, find the numbered egg that went into that place and traded the egg in the first place with the egg that belonged there. Repeat this process with the second place then the third place etc. After a minimum of 11 transpositions you would be done.