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Painting Cubes

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?

Tri-colour

Six points are arranged in space so that no three are collinear. How many line segments can be formed by joining the points in pairs?

Cube Paths

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

Flagging

Age 11 to 14 Challenge Level:

How many tricolour flags are possible with 5 available colours such that two adjacent stripes must NOT be the same colour. What about 256 colours? flags

<-- Here's an example for 3 colours.