Teaser 2784: Three lives
14 February 2016
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From The Sunday Times, 31st January 2016 [link]
I think of a whole number from 1 to 20 inclusive and Andy has to try to guess the number. He starts with three lives and makes successive guesses: after each guess I tell him whether it is right or too low or too high. If it is too high he loses one of his lives. To win the game he has to guess my number before his lives run out. He has developed the best possible strategy and can always win with a certain number of guesses or fewer. In fact no-one could be sure of winning with fewer guesses than that “certain number”.
What is that “certain number”?