Counting Theory
It's pretty simple when you get down to it: 10 pidgeons won't fit in 9 pidgeon holes. You can't compress every possible file because that means another file would become displaced. Always, a subset of possible files will increase in size due to compression technique. Certainly, a file of 4 billion zeros can be compressed by your magic RLE program much more heavily than something standard like winzip or gzip, but this technique won't work as well for just about any other kind of file. This is also why reapplied compression won't work, and there exists no magic algorithm that can reduce all data.
If you feel you can, try the challenge at DataCompression.
