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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?

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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?

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Estimating Angles

How good are you at estimating angles?

Angular Reflection

Age 11 to 14 Short Challenge Level:

As $OQ$ is the reflection of $OP$ in $OM$, $\angle QOM = \angle POM$.

Similarly, $\angle RON = \angle PON$.

Hence reflex $\angle QOR = 2 \times \angle MON = 260^{\circ}$

Therefore $\angle QOR =360^{\circ} - 260^{\circ} = 100^{\circ}$.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.