This is a variation on the classic problem of changing one word into another, one letter at a time. In this variation you may add and remove letters as well as change letters. You may also make more than one change per step. The catch is that it costs you 2^n points for each step, where n is the number of changes (except for n=1 which costs only 1 point).

For example: HINTS may be changed into SOLVE by
hints
shines (4 pts) add s;t->e
shine (1 pt) rem s
solve (8 pts) hin->olv
for a total of 13 pts

or
hints
hint (1)
hunt (1)
hone (4)
hole (1)
sole (1)
solve (1)
for a total of 9 points

The challenge in this case is to morph PROBLEM into SOLUTION in as few points as possible. I've managed to get it down to 21. Good luck and enjoy!

Just for fun you could try changing LEAD into GOLD (easy) or WATER into WINE (a little harder).