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.

The last day for sending in solutions to our live problems is Monday 15 March. 

Dozens live

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

Number Rules - OK live

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

Take Three from Five live

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

Always Perfect live

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.