Combinations

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

Semaphore is a way to signal the alphabet using two flags. You might want to send a message that contains more than just letters. How many other symbols could you send using this code?

The machine I use to produce Braille messages is faulty and one of the pins that makes a raised dot is not working. I typed a short message in Braille. Can you work out what it really says?

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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?

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?

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?

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?