Cubes and cuboids

problem

All Tied Up

Age

14 to 16

Challenge level

A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
problem

Interpenetrating Solids

Age

16 to 18

Challenge level

This problem provides training in visualisation and representation of 3D shapes. You will need to imagine rotating cubes, squashing cubes and even superimposing cubes!
problem

All in the Mind

Age

11 to 14

Challenge level

Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?
problem

Painting Cubes

Age

11 to 14

Challenge level

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

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

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

Cheese Cutting

Age

16 to 18

Challenge level

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

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

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

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