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How many loops of string have been used to make these patterns?

Look at some of the patterns in the Olympic Opening ceremonies and see what shapes you can spot.

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

Can you complete this calculation by filling in the missing numbers?

Can you come up with a system for describing where any of these drawers are?

Explore the triangles that can be made with seven sticks of the same length.

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

How many models can you find which obey these rules?

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?

Find the largest integer which divides every member of the following sequence: 1^5-1, 2^5-2, 3^5-3, ... n^5-n.