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Two infinitely intelligent Martians were walking back after missing their stop on a number 19 bus. "Let's have a game of Finchley Central," one Martian suggested to the other. "Good idea," said the other. "I'll go first."

Finchley Central (FC) is one of the most popular pastimes on Mars. The rules are simple:

1) The game is played between two gentlemen.

2) The players move alternately, by naming a station on the London underground system.

3) No station may be named more than once.

4) The first person to say "Finchley Central" wins.

It may seem that a player can say "Finchley Central" at the start, but (see rule 1) no gentleman would play so unsportingly. A polite victory is gained only by saying "Finchley Central" on the move before the opponent would have if you didn't.

So, for example, if there are only two stations left unnamed, the FC move is a perfect, gentlemanly winner, because if you don't say it, the opponent will have to.

But going back one move, when three stations remained, your opponent could have said FC because if he didn't, you, as we have just seen, would have.

Such thoughts passed through the mind of our Martian as he pondered his first move. "The inductive argument shows," he mused, "that if FC may be played at move n, then it may be played at move n-1. It must be played when n=1, I therefore start the game with..."

A copy of Chambers Encyclopaedia Dictionary awaits the best account of how the game went. Entries should be sent to: Martian Pastimes, the Independent, 1 Canada Square, Canary Wharf, London E14 5DL to arrive by 2 Aug.

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