On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?
At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?
How good are you at estimating angles?
What is the obtuse angle between the hands of a clock at 6 minutes past 8 o'clock?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.