Cool game – 20 questions – and how it works

Twenty Questions is a popular game which encourages deductive reasoning. Usually, one person is chosen to be the answerer. That person chooses a subject but does not reveal this to the others. All other players are questioners. They each take turns asking a question which can be answered with a simple “Yes” or “No”. Lying is not allowed, as it would ruin the game. If a questioner guesses the correct answer, that questioner wins and becomes the answerer for the next round. If 20 questions are asked without a correct guess, then the answerer has stumped the questioners and gets to be the answerer for another round.

20 questions

The above game is called 20Q and you can play it online at

Now for some math:
game is often used as an example when teaching students about
information theory. Mathematically, if each question is structured to
eliminate half the objects, 20 questions will allow the questioner to
distinguish between 2^20 or 1,048,576 objects. Thus, the best strategy
for 20 Questions is to ask questions that will split the field of
remaining possibilities roughly in half each time. This process is
analogous to a binary search algorithm in computer science.

** Note: Some posts on Math-Fail are user-submitted and NOT verified by the admin of the site before publication. If you find this post to be distasteful, non-math related, ?or something worse?, then definitely leave a comment letting me know. Thanks very much! Mike **

1 Star2 Stars3 Stars4 Stars5 Stars (No Ratings Yet)


  1. cool!!! 😛

    Thumb up 0 Thumb down 0