Interesting. The actual transform on a block of data such that the input is the output; i.e. x=h(x) is an identity, has no solution.

But, he's asking for the hash of a 32-character hex string representation of the original value. That is, x=h(f(x)) where f(x) expresses the 128-bit integer as a hex string.

I also notice that he didn't specify that f(x) is one-to-one, although his examples used lower-case letters. You could use an upper-case letter or lower-case for the same meaning in any position. So each value can have anywhere between 1 and 4,294,967,296 (inclusive) string representations. That opens up the ballpark more and increases the probability of such a value existing.

—John