Q: What is the shortest string that contains all the numbers from 0000 to 9999.

Probably not the shortest, but likely close:

perl -MCompress::Bzip2 -e "
print Compress::Bzip2::compress('all the numbers from 0000 to 9999')"
[download]

----
I wanted to explore how Perl's closures can be manipulated, and ended up creating an object system by accident.
-- Schemer

Note: All code is untested, unless otherwise stated