Generally, you can't compress every n-bit file into an (n-1) bit program because there are twice as many n-bit files as (n-1) bit programs. So the average n-bi

Generally, you can't compress every n-bit file into an (n-1) bit program because there are twice as many n-bit files as (n-1) bit programs. So the average n-bit file is not compressible. On the other hand, there are clearly some files that are highly compressible, and many that are at least a little bit compressible, so it's not as impossible as the challenge issuer made it sound. I'm not sure how you'd calculate this, but if more than 1 in 50 random files were somewhat compressible then it would be a bad bet to issue.