On: The $5000 Compression Challenge

[yk]

Actually even that is not feasible:

Assume that you split a m byte string into k byte decompressor and l byte input data. If k+l < m, that is you actually compress, then there are only 2^(k+l) possible output strings. And since

    sum_{i=0}^{m-1} 2^i = 2^m -1

there exists at least one string in the space of m character strings which can not be compressed by any algorithm.

[bagels → yk]

Yes, knowing which string(s) to choose which have this property as the challenge giver is the hard part.