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.