On a trip from Dayton, OH to Richmond, VA, I was driving through Charleston, WV and a few minutes after passing the capitol building of this Appalachian state I remembered that Charleston was indeed the capitol. Because I was on my way to Richmond, I suddenly started thinking of the possibility of visiting all state capitals and their corresponding capitals. “How much time would it take?”, “What would be the most efficient Route?” were all questions that popped into my head.
Consequently, I started wondering about the possibility of answering the question through computation. Maybe, I could use programming to answer the questions by simply calculating every simple possibility available. Initially (and perhaps as an omen to my lack of knowledge in math), I thought the number of possibilities would simple be 48 * 48. That would equal 2304 possibilities.
A few days later I started writing some code to figure out, at least, if my previous calculations were correct. Thinking about it a bit, I figured that the calculation was not 48 * 48, but rather 48 to the 48th power. That small mistake dramatically changed everything. Now, rather than having the previous 2304 possibilities, I now had 5.0070207826345931917453702524957e+80 (Still incorrect, but closer). Quite a bit more.