How many times do the Hour/Minute/Second hands overlap a day?

Just saw the hands overlap exactly, and thought to myself:  How many times do the Hour/Minute/Second hands overlap?  (And) What are the exact times (HH:MM:SS)?

I don't have prizes, but a fun little math problem to pass the time if you're having a bad monday (no googling!)

Edit: I do have the answer.  Wasn't too complicated to figure out, but there is a long way, and an easy way to figure this out!

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Is it once for each hour? Twenty four for the day? Besides midnight i couldn’t tell you which other times or how to figure them out.

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When I joined WC I was told there wouldn't be any math.