Problems

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

What's the largest volume of box you can make from a square of paper?

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

Are these games fair? How can you tell?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?