On Time

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?

Right Time

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?

Estimating Angles

How good are you at estimating angles?

Robo-turn

Age 11 to 14 Short Challenge Level:

A robot, which is initially facing North, is programmed to travel 5m then turn through $10^{\circ}$, travel 5m then turn through $20^{\circ}$ clockwise, travel 5m then turn through $30^{\circ}$ clockwise, and so on. Each move consists of moving 5m in a straight line and then turning clockwise through an angle which increases by $10^{\circ}$ clockwise at each move.

How far has it travelled by the time it is first facing due East at the end of a move?

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