The $5000 Compression Challenge (2001)

If a randomly-generated file happened to contain some redundancy through sheer chance, you could hand-craft a compressor to take advantage of it. This compressor would not work in general for random data, but it could work for this one particular case.

It's a bet worth taking, because the payoff, 50:1 ($5,000 to $100), is pretty good. Play the game 50 times and you might get a file you could compress.

The challenge, then, would be for the person offering the bet to generate a really random file that contained no such redundancy. That might not be easy.

Actually this would work perfectly if you knew it was generated in a single pass by a known random number generator and you had tons of time to brute force it.

If the file were generated by a natural source of entropy then forget it.

Or even if modified in a trivial way like adding 1 to every byte.

Seeds are something like 32 bits, though it depends on the exact implementation. But not the length of files.