Use a sorting algorithm

Question

Consider the numerical 20 questions game. In this game, player 1 thinks of a number in the range 1 to n. Player 2 has to figure out this number by asking the fewest number of true/false questions.Assume that nobody cheats. i. What is an optimal strategy if n in known? ii. What is a good strategy is n is not known?

Binary search if n is known, otherwise the problem becomes more interesting. — IVlad
– IVlad, Commented Feb 21, 2013 at 13:39
@IVlad if upper bound is unknown, first doubling from 1(to find a upper bound), then halving(to find the exact number). — Hui Zheng
– Hui Zheng, Commented Feb 21, 2013 at 13:50

Hui Zheng · Accepted Answer · 2013-02-21 13:59:54Z

7

Please refer to this wiki: binary search for number guessing game.

If n is known, use binary search algorithm to find it, so asked questions is not more than floor(log2(n)).

If n is unknown, you can first find an upper bound by repeated doubling, then apply binary search. It's clear that asked questions is not more than 2 * floor(log2(k)) + 1, where k is the unknown selected number.

edited Feb 21, 2013 at 13:59

answered Feb 21, 2013 at 13:36

Hui Zheng

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2 Comments

ECR Over a year ago

yeah! thanks for that! but in the question, it says that, it should be done in Optimal and in Good strategy!! :(

Hui Zheng Over a year ago

I updated my answer to give the time complexity for both cases. They are proved to be optimal and surely good strategies.

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