Mathematicians often talk about the importance of working systematically on a problem, rather than approaching it in a random, unstructured way. The tasks in this feature have been chosen because systematic approaches will offer the most efficient routes to the solutions.
In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?