Why was double used as opposed to long? My solution is valid in my opinion, but because jitter can creep into a floating point number over multiple operations, sometimes it fails the random test.

I suggest modifying the second given example to be more different in the appearance count from the first example to cut down on the chance the reader leaves with the idea that the character string is only valid if every character appears twice.

Example modification:
"abcabcab" is NOT a valid word because 'a' appears thrice, 'b' appears thrice, but 'c' only appears twice!

Because C89