Copyright © University of Cambridge. All rights reserved.

## 'Nine Colours' printed from http://nrich.maths.org/

### Why do this problem?

This is an engaging problem that challenges students to work in
3 dimensions and to use different representations of the cube. It
can be used to encourage students to persevere, collaborate, work
systematically and reason logically.

### Possible approach

Introduce the task by
challenging the students to create an anti-rubik's cube.

Offer them multilink
cubes (plastic coloured cubes that fix together), pencil and paper
and the computer interactivity so that they have a choice of ways
in which to approach the problem.

Let students pursue their own attempts to orientate themselves
within this context, but attention may be drawn, at well-judged
moments, to the number of faces that cubes in individual positions
will have 'visible'.

### Key questions

- Some of the 27 cubes have faces that are invisible from the
'outside' of the large cube. How many cubes have no 'visible'
faces? One face visible? Two faces visible? Three faces
visible?

- If one colour appears in a corner, where will the other two
cubes of the same colour need to appear?

- There will be a cube of some colour at the centre. Where else
will cubes of that colour need to be positioned?

### Possible extension

If students have chosen
how to solve the problem from a range of possibilities (ie.
multilink cubes, pencil and paper or the computer interactivity)
challenge them to solve the puzzle again from scratch using a
different approach.

### Possible support

Students could attempt

Painted Cube
before trying this problem.

Handouts for teachers are
available here (

word document,

pdf document),
with the problem on one side and the notes on the
other.