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I see, I mixed up the adavance of the hour hand with the elapsed time for each cycle. And I calculated period incorrectly for the second part in my previous post. Still, after the corrections, I get a different answer. My hour and minute hands will meet a lot sooner. Why rejecting the occurences where the clock hands meet at 12 in a mid-cycle? I see nothing in the OP prohibiting that. In fact, the clock hands will meet again at 12 on a mid-cycle before they do so after a whole number of cycles.

You know you're a grammar Nazi when you're me. Simply bow to the inevitable and declare me Fuhrer.