Adventures with Numbers

Number theory - the study of the natural numbers - is not usually studied at school, but it is a rich source of interesting problems which can lead to surprising results.  The problems in this feature will offer you the opportunity to notice patterns, conjecture, generalise and prove results.

Many results can be explained by applying lower secondary school algebraic techniques, and many can also be explained using pictorial representations.


Age 7 to 14
Challenge Level
Can you select the missing digit(s) to find the largest multiple?

Number Rules - OK 

Age 14 to 16
Challenge Level
Can you produce convincing arguments that a selection of statements about numbers are true?

Take Three from Five 

Age 11 to 16
Challenge Level
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

Always Perfect 

Age 14 to 18
Challenge Level
Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

We are very grateful to the Heilbronn Institute for Mathematical Research for their generous support for the development of these resources.