I suspect the world would be better if that percentage were even greater.
Surprise, Success!
My exhaustive testing indicated that the shortest path to the goal position in Scarne’s challenge was at least 71 moves long. I relaxed the criteria a bit, and obtained a solution which requires 72 moves, which (if I haven’t made an off by one error, still checking that out) is an actual minimal cost solution!
This solution doesn’t actually include the 5 hopping moves at the beginning (it complicates the calculation of the heurstic values and slows down the search), but I suspect I’ll get that figured out someday soon. Enjoy!
Comment from Mark
Time 8/31/2002 at 9:44 pm
I’ve implemented the first five moves being hopped, and have found a 58 move solution.