I think that it is DP-problem
We consider 2^16 states from 0 to final=2^16-1
Before we make precalculation finding for each draught
finite possible moves just as adjacent to some
another draught and bisectors between adjacent rays
Anywhere we must use eps≈0.0000001 as precision level.
Having found all possible moves we can easy reduce state k
to states with few value because one move make number of draughts smaller.
Finding all possibilities we must consider adjacent rays to draughts with the same color
as now active  draught.

Edited by author 27.06.2007 13:46

I think, it is impolite to explain solutions of good problems here in forum. Of course, greedy algo doesn't work here...

This is an old problem and beginers need
clear plan before starting to solve.

I agree with svr. Things required to solve this problem are quite conceptual, so it's ok to tell them in the forum.