At noon and at midnight, the long and short hands of a clock are together. Between noon and midnight, how many times does the long hand pass the short hand?
Answer
The long hand passes the short hand only eleven times and not twelve times.
The long hand passes the short hand at noon, and between the times 1-2 pm, 2-3 pm, 3-4 pm, 4-5 pm, 5-6 pm, 6-7 pm, 7-8 pm, 8-9 pm, 9-10 pm, 10-11 pm – a total of eleven times. Note that the long hand does not pass the short hand between 11 pm and 12 am, it just meets the short hand at 12 am.