Combinations

problem

Flora the Florist

Age

14 to 16

Challenge level

1 out of 3

Flora has roses in three colours. What is the greatest number of identical bunches she can make, using all the flowers?
problem

Coin Tossing Games

Age

14 to 16

Challenge level

2 out of 3

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?
problem

Cross-Country Race

Age

14 to 16

Challenge level

2 out of 3

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

The Olympic Torch Tour

Age

14 to 16

Challenge level

2 out of 3

Imagine you had to plan the tour for the Olympic Torch. Is there an efficient way of choosing the shortest possible route?
problem

Scratch Cards

Age

14 to 16

Challenge level

3 out of 3

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?
problem

Factoring a Million

Age

14 to 16

Challenge level

3 out of 3

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

Spectrometry Detective

Age

16 to 18

Challenge level

1 out of 3

From the atomic masses recorded in a mass spectrometry analysis can you deduce the possible form of these compounds?
article
Creative Approaches to Mathematics Across the Curriculum

Suggestions for teachers about exploring maths in different contexts: art, history and so on
article
The Secret World of Codes and Code Breaking

When you think of spies and secret agents, you probably wouldn’t think of mathematics. Some of the most famous code breakers in history have been mathematicians.
article
Binomial Coefficients

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.