SOLUTION: Keith and Chi-An are playing a game. Keith chooses a positive integer less than 100. Chi-An then tries to guess Keith's number by asking questions to which Keith answers yes or no.

Question 81628: Keith and Chi-An are playing a game. Keith chooses a positive integer less than 100. Chi-An then tries to guess Keith's number by asking questions to which Keith answers yes or no. What is the number of questions Chi-An must ask so that, even if she is unlucky, she will always be able to identify the number?
Answer by rajagopalan(148) (Show Source):
You can put this solution on YOUR website!
The answer is got by logical conclusion like this:
The method is halving & doubling
Qn 1 ..Is your number say Less than 50...If Yes
Qn 2 ..Is your number say Less than 25...If Yes
Qn 3 ..Is your number say Less than 13...If Yes
Qn 4 ..Is your number say Less than 07...If Yes
Qn 5 ..Is your number say Less than 04...If Yes
Qn 6 ..Is your number say Less than 02...If Yes
Qn 7 ..Is your number say equal to 01... Yes.
If for Qn no 1 it is "No" you add 25 (50% 0f the difference) & ask for <75 & so on.
Literally the number of qns should not exceed 7.
And for a number leass than 200 the number of Qns needed is 8.
So your answer : 7 questions.