### A Problem of Time

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?

### Fit for Photocopying

Explore the relationships between different paper sizes.

### Back in Time

How many times a day does a 24 hour digital clock look the same when reflected in a horizontal line?

# Coloured Black

##### Age 14 to 16 Short Challenge Level:

A square ink stamp has sides of length 1 cm.

It is covered in black ink and carefully placed in the middle of a piece of white paper.

The stamp is then rotated $180^o$ about one of its corners so that all of the square remains in contact with the paper throughout the turn, leaving a black trail.

The stamp is then removed from the paper.

What area of paper, in cm$^2$, is coloured black?

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.