> But the challenge isn't to compress random strings, the challenge is to compress a specific random string.

I agree and I think that this challenge is vulnerable albeit very difficult but not impossible, at least not via the pigeonhole principle.

To be clear, the pigeonhole principle says for a given compression aglo and an input file of size n the output file must get bigger than n for some inputs of size n, i.e. it cannot compress all possible permutations of size n.

However, the way the challenge is setup it is saying; given a specific random file of size n, find an algo that can compress the file so that the output plus decompressor is less than the input file. The pigeonhole principle does not say this is impossible. Granted, finding the algo that does this may mean solving P=NP or may take 10^32 lifetimes of the universe in calc time to find it but in principle it is not impossible.

I admit, my understanding may be wrong and would really appreciate it if someone can explain to me my error here.