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?
Noah saw 12 legs walk by into the Ark. How many creatures did he see?
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
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!
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.
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?
Christina and Joanna worked out what the shapes had in common.
Christina has also suggested some sets of her own.
Go to last month's problems to see more solutions.
What are rich tasks and contexts and why do they matter?
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