Combinations

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do this?

Eight children enter the autumn cross-country race at school. How many possible ways could they come in at first, second and third places?

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 how many ways can the number 1 000 000 be expressed as the product of three positive integers?

Is it possible to use all 28 dominoes arranging them in squares of four? What patterns can you see in the solution(s)?