There is a flaw in your random sequence approach; lets see if you can find it? Its a fun thinking exercise. You can estimate the minimum bound on compression

There is a flaw in your random sequence approach; lets see if you can find it? Its a fun thinking exercise. You can estimate the minimum bound on compression using Shannon's estimate http://en.wikipedia.org/wiki/Entropy_(information_theory) http://en.wikipedia.org/wiki/Entropy_(information_theory) An excellent problem for hobby coders is the Hutter Prize. Even if you don't win - and that'd be front page HN news if you did - its a really fun challenge and an excellent introduction to compression: http://prize.hutter1.net/ http://prize.hutter1.net/ Also worth googling is Kolmogorov complexity.