Cubes and cuboids

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

Crawl Around the Cube

Age

11 to 14

Challenge level

Weekly Problem 37 - 2010
An ant is crawling around the edges of a cube. From the description of his path, can you predict when he will return to his starting point?
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.
problem

Four Layers

Age

5 to 11

Challenge level

Can you create more models that follow these rules?
problem

Multilink Cubes

Age

7 to 11

Challenge level

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

Double Your Popcorn, Double Your Pleasure

Age

7 to 11

Challenge level

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.