Discussion
How many times in 24 hours are the hands of a clock in opposite directions ?
Answer: A
Correct answer: 22
The hands point in opposite directions once for every full \(360°\) the minute hand gains on the hour hand. That gain happens 11 times in 12 hours, so the hands are opposite 11 times in 12 hours and 22 times in 24 hours.
The same reasoning gives 22 coincidences in 24 hours, since each relative revolution produces exactly one of each.
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