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# Out of Sync

Albert Einstein was standing on the station platform thinking about relativity when he noticed that he could see two station clocks. Each clock was digital, showing only hours and minutes.

He observed that the display on one clock changed to the next minute $10$ seconds before the correct time, whereas the display on the other clock changed to the next minute $10$ seconds after the correct time.

For what fraction of the day did the clocks show the same time?

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Albert Einstein was standing on the station platform thinking about relativity when he noticed that he could see two station clocks. Each clock was digital, showing only hours and minutes.

He observed that the display on one clock changed to the next minute $10$ seconds before the correct time, whereas the display on the other clock changed to the next minute $10$ seconds after the correct time.

For what fraction of the day did the clocks show the same time?

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.

Two trains set off at the same time from each end of a single straight railway line. A very fast bee starts off in front of the first train and flies continuously back and forth between the two trains. How far does Sidney fly before he is squashed between the two trains?

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

Which segment on a digital clock is lit most each day? Which segment is lit least? Does it make any difference if it is set to 12 hours or 24 hours?