Chomp is a simple two-dimensional game, played as follows.
Cookies are set out on a rectangular grid. The bottom left cookie is poisoned.
Two players take it in turn to "chomp" - that is, to eat one of the remaining cookies, plus all the cookies above and to the right of that cookie.
Last October, two mathematicians won £1m when it was revealed that they were the first to solve the Eternity jigsaw puzzle. It had taken them six months and a generous helping of mathematical analysis. Mark Wainwright meets the pair and finds out how they did it.
There are many sorts of games played in a "bunco booth", where a trickster or sleight-of-hand expert tries to relieve you of your money by getting you to place bets - on which cup the ball is under, for instance, or where the queen of spades is. Lots of these games can be analysed using probability theory, and it soon becomes obvious that the games are tipped heavily in favour of the trickster!
Arguably, the exponential function crops up more than any other when using mathematics to describe the physical world. In the first of two articles on physical phenomena which obey exponential laws, Ian Garbett discusses light attenuation - the way in which light decreases in intensity as it passes through a medium.
The idea is this. To start with, you will choose an envelope at random, say by tossing a coin, and look at its contents, which is a cheque for some number - say n. (By randomising like this, you can be sure I haven't subconsciously induced you to prefer one envelope or the other.) You want to make sure that the bigger the number is, the more likely you are to keep it, in other words, the less likely you are to swap.