Solution:
I believe the solution is as follows (assume initial configuration to be an empty bucket at the top and a bucket with the stone in it at the bottom):
1. Prince goes down, rock goes up.
2. Queen goes down, Prince goes up.
3. (the rock is dropped from the top of the tower)
4. King goes down, Queen and rock go up.
5. (the rock is dropped from the top of the tower)
6. Prince goes down, rock goes up.
7. Queen goes down, Prince comes up.
8. (the rock is dropped from the top of the tower)
9. Prince goes down, rock goes up.
2. Queen goes down, Prince goes up.
3. (the rock is dropped from the top of the tower)
4. King goes down, Queen and rock go up.
5. (the rock is dropped from the top of the tower)
6. Prince goes down, rock goes up.
7. Queen goes down, Prince comes up.
8. (the rock is dropped from the top of the tower)
9. Prince goes down, rock goes up.
POST YOUR OPINION IF YOU HAVE BETTER SOLUTION
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