Smith and Jones each secretly write down a number between 1 and 100. The object of the game is to guess the other player’s number first. Questions may be asked concerning the opponent’s number provided that they can be answered truthfully by a YES or a NO. A player is allowed to continue asking questions so long as he receives YES answers. The first NO answer transfers the role of questioner to the opponent. The conservative “Twenty Questions” strategy of questioning in such a manner as to most nearly equalize the chances of YES and NO answers is most effective in that particular game. Using it, you can, in only 20 questions, invariably pinpoint any number in the range of 1 to 500,000. But in the game outlined above, this may not be the best way to proceed. Suppose you are the first player. What will your questioning strategy be, and how much of an advantage do you feel you have over your opponent?
REVEAL THE ANSWER
Your strategy should be quite different from that pursued in Twenty Questions. One way to begin is to start with the question, Is your number bigger than 1? If you get a YES response, your next question will be, Is your number bigger than 2? and so on. In this manner, the first NO answer you receive will pinpoint your opponents number, which you will promptly guess the next time you assume the role of questioner. The only way your opponent can win, therefore, is to guess your number on his first round of questions. His chance of doing this is 1 out of 100, 50 your advantage in this game, as first questioner, is 99 to 1. As the size of the range of numbers increases, the first players advantage increases correspondingly.
