Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

A church hymn book contains 700 hymns. The numbers of the hymns are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Christina and Joanna worked out what the shapes had in common. Christina has also suggested some sets of her own.

The very problem with problems, namely that they should result in you being stuck, is at the heart of what problem-solving is about. In this article for teachers I talk about just a few of the other problems with problems that make them such a rich source of mathematics.