Are both these sentences correct, and do they mean the same:
a) "I don't know who did this, but I have a hint."
b) "I don't know who did this, but I have a clue."
Christine Christiea) "I don't know who did this, but I have a hint."
That's possible, but it suggests someone provided me with a hint.
Christine Christieb) "I don't know who did this, but I have a clue."
That's also possible, but it suggests that someone or something has given me a clue.
Consider the more common:
I don't know who did this, but I have a (fair) idea.
Comments
I think you mean "I don't know who did this, but I can guess." Neither of your two sentences work for that. That aside, "hint" is wrong there, and "have a clue" is possible but only if you actually have one. "Have some clue" would be more like it by analogy with the ordinary "have some idea", but "clue" is somewhat slangy there.