### Trice

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

### Nine Colours

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

### Marbles in a Box

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

# Cubes on a Cube

##### Stage: 3 Short Challenge Level:

A cube has each of its faces covered by one face of an identical cube, making a solid as shown. The volume of the solid is $875\text{cm}^3$.

What, in $\text{cm}^2$, is the surface area of the solid?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.
View the archive of all weekly problems grouped by curriculum topic

View the previous week's solution