Flora has roses in three colours. What is the greatest number of identical bunches she can make, using all the flowers?
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?
Eight children enter the autumn cross-country race at school. How many possible ways could they come in at first, second and third places?
Imagine you had to plan the tour for the Olympic Torch. Is there an efficient way of choosing the shortest possible route?
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?
