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Twenty questions

Twenty questions is a two-person or multi-person guessing game. It is also known as Animal, vegetable or mineral?

One person thinks of an object, and says whether it is "animal" (including humans), vegetable, or mineral. The guesser or guessers must determine what this object is, by sequentially asking 20 yes-or-no questions about the object, which are answered either "yes" or "no". For example: "is it a person?", "is it someone I know?" ... If the guessers manages to work out what the object is after twenty questions, then they win. Otherwise, the person who thought of the object wins, and reveals what the object was.

The optimal strategy for the guesser is to use a binary search, i.e. to make each question to eliminate half the remaining possibilities. That is not necessarily the same as eliminating half the remaining possible answers. Suppose that we have identified that the answer is the name of a Welshman, and we know that half of all Welshman are called Jones and the other 5 million Welshman all have different surnames, then an appropriate question would be "is his surname Jones?"(*). The fact that the game can be played successfully (i.e. that it is not a foregone conclusion who will win) suggests that the information (as measured by Shannon's entropy statistic) required to identify an arbitrary object is about 20 bits. The game is often used as an example when teaching people about information theory.

The optimal strategy translates into the tactic of asking very broad questions initially, such as "Are they male or female?", and asking very narrow questions towards the end, such as "Is she a character in Star Trek?"

The game was turned into a popular radio programme, of the same name, by the BBC in the 1950s. The object to be guessed was revealed to the audience by a "mystery voice".

(*)This should not be taken as an accurate description of the distribution of surnames in Wales.

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