How many times do a clock's hands perfectly overlap in twelve hours?
A clock has an hour hand and a minute hand, both moving continuously but at different speeds. Over a full 12-hour period, how many times do the two hands point in exactly the same direction?
Reveal the answer
Eleven times, not twelve. The minute hand gains a full lap on the hour hand every 12/11 hours, about 65 minutes and 5 seconds, not every hour, because the hour hand is also creeping forward while the minute hand catches up; they coincide at 12:00, roughly 1:05, 2:11 and so on, returning to 12:00 only after 11 overlaps. This is a classic recreational-mathematics puzzle usually called the clock angle problem.