Cubes and cuboids

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
Favourite

Cubes cut into four pieces

Age

5 to 7

Challenge level

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?
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
Favourite

The third dimension

Age

5 to 11

Challenge level

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
problem

Four layers

Age

5 to 11

Challenge level

Can you create more models that follow these rules?
problem
Favourite

Always, sometimes or never? Shape

Age

7 to 11

Challenge level

Are these statements always true, sometimes true or never true?
problem

Multilink cubes

Age

7 to 11

Challenge level

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