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Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

Can you prove that triangles are right-angled when $a^2+b^2=c^2$?

Can you justify this equation involving three angles?

Can Jo make a gym bag for her trainers from the piece of fabric she has?

Here you have an opportunity to explore the proofs of the laws of logarithms.

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Can you work out where the blue-and-red brick roads end?