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Clock Hands

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

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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: Challenge Level:1
In each minute, the two clocks showed the same time for $40$ seconds, i.e. they showed the same time for ${40\over60} = {2\over3}$ of the day.

This problem is taken from the UKMT Mathematical Challenges.