Combinations

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

To win on a scratch card you have to uncover three numbers that add up to more than fifteen. What is the probability of winning a prize?

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?