Cubes and cuboids

problem

Painting Cubes

Age

11 to 14

Challenge level

3 out of 3

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?
problem

Take Ten

Age

11 to 14

Challenge level

3 out of 3

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?
problem

Cubic Conundrum

Age

7 to 16

Challenge level

3 out of 3

Which of the following cubes can be made from these nets?
problem

Cheese Cutting

Age

16 to 18

Challenge level

3 out of 3

In this problem we see how many pieces we can cut a cube of cheese into using a limited number of slices. How many pieces will you be able to make?
problem

Start Cube Drilling

Age

5 to 7

Challenge level

3 out of 3

Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?
problem

Holes

Age

5 to 11

Challenge level

1 out of 3

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?
problem

Triple Cubes

Age

5 to 11

Challenge level

1 out of 3

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
problem

Four Layers

Age

5 to 11

Challenge level

3 out of 3

Can you create more models that follow these rules?
problem

Multilink Cubes

Age

7 to 11

Challenge level

1 out of 3

If you had 36 cubes, what different cuboids could you make?
problem

Cubes

Age

7 to 11

Challenge level

1 out of 3

How many faces can you see when you arrange these three cubes in different ways?