"Observe the time, would you, Watson, old chap?"
I did as instructed and glanced at the large grandfather clock standing in the corner. "Just a little after 4.42, Holmes."
He nodded, "So when the position of the hands are exactly reversed, it will be a bit after 8.23".
"Just so," I agreed.
"Given that the position of the hour hand is fixed precisely, moment buy moment, by the exact movement of the minute hand, there are only a limited number of times in any given period when the positions of the hands will exactly swap locations. If it was 4.45, there will be no reverse alignment".
"I can see that," I said.
"So how many times do you think the hands of a clock will exactly reverse themselves between 3pm and midnight?"