### Times

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

### Clock Hands

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

### Ten Green Bottles

Do you know the rhyme about ten green bottles hanging on a wall? If the first bottle fell at ten past five and the others fell down at 5 minute intervals, what time would the last bottle fall down?

# Out of Sync

##### Stage: 2 and 3 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

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?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.