(In reply to solution
by Dej Mar)
That part is interesting but it's phrased more as an observation rather than a proof. Regardless, you chose the easy half to prove -- the statement says "if and only if".
To prove the other half, one needs to show at least one light will always remain on for every value of n which is not a power of two. Thus the only values of n where they will all turn off at some point on the future are powers of two.
Posted by Gamer
on 2010-09-03 04:17:50