There are eight doors in front of you labeled A through H. Behind one of the doors is a prize. A guard is aware of the prize’s location but will only answer yes or no questions. What is the minimum number of questions you can ask to guarantee choosing the correct door?
(For a challenge, find a general formula for the number of questions you’d need depending on how many doors there are.)
Suppose you first ask, “Is the prize hiding behind door B?” If the guard answers yes, you’ve gotten the answer in one try, but if not, you still have seven doors to choose between. To find the smallest number of questions that will suffice no matter what, you need to assume the worst-case scenario—that after each question the smaller portion of doors will be eliminated. So the best questions are those that are guaranteed to eliminate half of the doors no matter what the guard’s answer is. (For example: “Is the prize behind a door that is labeled A, B, C or D?”) Eight can be split in half three times: the first question will reduce the eight doors to four possibilities, the next will reduce it to two, and the final question will leave only one door remaining—behind which is your prize!
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