How many times do a clock's hour and minute hands exactly overlap in 12 hours?
A clock's hour hand and minute hand start together at 12:00. As the hours pass, the minute hand keeps lapping the slower hour hand. Most people's gut answer is 12 — once per hour. Is that right, and if not, why not?
Reveal the answer
Only 11 times, not 12. Between 11:00 and 1:00 the hands coincide just once, exactly at 12:00 — there's no separate overlap squeezed in before or after. Each overlap actually happens every 12/11 hours (about 65 minutes 27 seconds), a classic trap in aptitude-test clock puzzles.
— Wikipedia contributors, Clock angle problem — Encyclopedia entry; classic aptitude-test puzzle