FILE No.164Unsolved
A 12-hour analog clock, set to the correct time, loses one minute every day.
After how many days will this clock show the correct time again?
If you get stuck, open the hints one at a time, in order.
How many minutes are in 12 hours?
What happens to the hands when the lag reaches 12 hours?
Think of it as losing one minute a day.
After how many days will this clock show the correct time again?
Choose the answer closest to the truth.
After 720 days
The answer is "After 720 days."
12 hours is 720 minutes. Losing one minute a day, it takes 720 days for the lag to build up to 720 minutes (12 hours). A 12-hour lag puts the hands back in the same positions, so it looks the same as the correct time.
At 360 days the lag is 6 hours; 1,440 days would be a 24-hour lag, but before that, at 720 days, the hands match once.
Because it is easy to confuse it with a 24-hour clock.
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