Combinations

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

I start my journey in Rio de Janeiro and visit all the cities as Hamilton described, passing through Canberra before Madrid, and then returning to Rio. What route could I have taken?

Squares of the type shown are sewn together to make a quilt. How many different quilts can be made?

How many 10-digit numbers containing only 1s, 2s and 3s can you write?

Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Using only the red and white rods, how many different ways are there to make up the other rods?

Weekly Problem 21 - 2011
How many ways can you paint this wall with four different colours?