Sunday Times Teaser 2784 – Three Lives

by Ian Kay

In a guessing game my friend has to guess a number that I have chosen between 1 and 20 inclusive.

He starts with three lives and loses one each time he guesses high, winning if he guesses my number before his lives run out. For each guess I tell him whether it is low, correct or high.

He has devised an optimal strategy and can always win with at most a certain number of guesses. In fact, no-one could be sure of winning with with fewer guesses than this.

What is this number of guesses?