Bill thought of the problem carefully.
Bill thought about the problem carefully.
Any difference could be?
Only difference is 'of' and 'about'. This means the answer is the difference between 'of' and 'about'.
of : a friend of mine, the leg of the table, sth consist of sth, remind A of B give hint, i.e., 'of' needs precedent before of and object after of, which means 'of' provides connection between specific two things and narrows sth down to specific information: A of B. So "think of sth" means think of specific B, the existance of B
about : about 10 mins gives hint, hid money about myself gives hint. about means scattered, i.e., not a fixed point. so 'think about X' means 'X' has some attrubutes around X and you think some of the attributes or the attributes.