Can you solve it? An Oxford University admissions question

Today’s puzzle concerns contestants in a fictitious game show trying to win £1m. It was also once given to a different sort of contestant competing for a different sort of prize: candidates applying to study joint philosophy degrees at Oxford university., and Computer Science and Philosophy. They were set the puzzle in their admissions interviews, as part of a back-and-forth discussion in which the interviewer may have given hints and asked probing questions.

The game begins with round 1, then proceeds with rounds 2, 3, and so on, for as many rounds as need be. On each round, each contestant has two choices:To send a message to the other contestant.To win the game you must both end the game on the same round, announcing the same colours. If only one of you ends the game, or you both end it announcing different colours, you lose.Clearly, you don’t end the game on round 1. That’s a self-evidently bad strategy.

In this ‘alternating’ version, a simple strategy presents itself. Your round 1 message could be: “I will declare red on round 2; if you also do we will win.” Or, if you are more cautious, you may say: “let’s declare red in round 3, please confirm in round 2”. Remember, the other contestant wants to cooperate, and so will follow your lead. You will both win the £1m by round 3.in the original puzzle, when both of you must send messages simultaneously.

When this puzzle was used in Oxford admissions interviews, the contestant was not expected to come up with a perfect answer straight away. For a start, there is no clear-cut, “best message” to ask in round 1, since the effectiveness of any message will depend on the message you receive, and there is no way that you can know that in advance. Rather, the puzzle led to an open-ended discussion of the issues involved.

Is it, how much do your parents earn?

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