For example, how do I solve for x such that md5(“The md5 of this sentence is [x].” = x? Is this possible with a reasonable amount of effort?
Are there any other common cryptographic hashes that make this easier or harder?
How to embed md5 sum of sentence in the sentence?
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Is this possible with a reasonable amount of effort?
No, at best brute force 2^128, at worst no.
Are there any other common cryptographic hashes that make this easier or harder?
SHA-3 or Skein allow a specified output size with a short output it would be easier. A longer hash output would be harder.