I remember there was an interesting problem @ school back when i was around 12 or so: how many times do you have to fold a piece of paper 0.5mm thick in order to cover the distance from the Earth to the Moon (roughly 330K Kilometers)?
Back then i didn't have a calculator, so i did the math by hand: you have to fold the piece of paper 42 times, and that more than covers the distance from the Earth to the Moon. My answer was actually wrong because i started from 1 and doubled it until reaching the distance to the Moon, not taking in to account the fact that the paper was 0.5mm thick and NOT 1mm, thus the correct answer is actually 43 and NOT 42 but, since apparently i was the only one to have tried to solve this problem, and having shown the papers where i did my math to the teachers, i managed to win a prize for my efforts, though i can't seem to remember what it was.
The OP's math problem reminds me of the above problem i just described.