Tessellate S.T.E.M.S. (2019) - Computer Science - School - Set 4 - Objective Problem 4

Probability Level 3

Rama and Sita play some game which goes as follows. Sita first think about a natural number between $1$ and $100$ . Rama asks questions to Sita, but Sita can only reply in ”yes” or ”no” . Sita is a honest lady, and never tells a lie. What is the least number of questions Rama needs to ask such that he always figure out the number, Sita thought about?

This problem is a part of Tessellate S.T.E.M.S (2019)

1 7 4 10

1 solution

Jordan Cahn
Dec 26, 2018

With every question, Rama can eliminate half of the possible numbers. Thus, in the worst case, it will take $2^n$ questions to narrow down the $100$ possibilities, where $n$ is our solution. $\lceil\log_2 100 \rceil = \boxed{7}$

Tessellate S.T.E.M.S. (2019) - Computer Science - School - Set 4 - Objective Problem 4

1 solution

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