Make the following exchanges of pairs: H-K, H-E, H-C, H-A, I-L, I-F,
I-D, K-L, G-J, J-A, F-K, L-E, D-K, E-F, E-D, E-B, B-K. It will be found
that, although the white counters can be moved to their proper places in
11 moves, if we omit all consideration of exchanges, yet the black
cannot be so moved in fewer than 17 moves. So we have to introduce waste
moves with the white counters to equal the minimum required by the
black. Thus fewer than 17 moves must be impossible. Some of the moves
are, of course, interchangeable.