When you get stuck, what strategies do you use to get unstuck? These problems will require some resilience and perseverance, so rise to the challenge, make good use of our hints, and see where determination can get you!

Challenge Level

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

Challenge Level

Under what circumstances can you rearrange a big square to make three smaller squares?

Challenge Level

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Challenge Level

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

Andrew Wiles, who famously proved Fermat's Last Theorem, talks about being a mathematician and dealing with being stuck.