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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."

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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.