File containing its own checksum

Question

Is it possible to create a file that will contain its own checksum (MD5, SHA1, whatever)? And to upset jokers I mean checksum in plain, not function calculating it.

Answer 1

If the question is asking whether a file can contain its own checksum (in addition to other content), the answer is trivially yes for fixed-size checksums, because a file could contain all possible checksum values.

If the question is whether a file could consist of its own checksum (and nothing else), it's trivial to construct a checksum algorithm that would make such a file impossible: for an n-byte checksum, take the binary representation of the first n bytes of the file and add 1. Since it's also trivial to construct a checksum that always encodes itself (i.e. do the above without adding 1), clearly there are some checksums that can encode themselves, and some that cannot. It would probably be quite difficult to tell which of these a standard checksum is.