A game in which players take it in turns to choose a number. Can you block your opponent?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Follow this recipe for sieving numbers and see what interesting patterns emerge.

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

These two group activities use mathematical reasoning - one is numerical, one geometric.

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

Can you make square numbers by adding two prime numbers together?

All strange numbers are prime. Every one digit prime number is strange and a number of two or more digits is strange if and only if so are the two numbers obtained from it by omitting either. . . .