perplexus.info :: General : Interval Guessing

Interval Guessing (Posted on 2019-10-21)

I am thinking of an integer in the interval [1-15]. You are to try to guess it by telling me intervals and I will tell you if my number lies in that interval.

For example if my number is 6 and you guess [6-9] I will tell yes but if you guess [7-11] I will tell you no but not if my number is higher or lower.

You win by guessing an interval of just one number and that number is my number. Find a strategy that minimizes the expected number of guesses.

No Solution Yet Submitted by Brian Smith

Rating: 5.0000 (1 votes)

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A note

Comment 10 of 10 |

The order of the integers is irrelevant.

Consider the example. If your first guess is [7-11] and the number is 6. A response of no leaves you with the set {1,2,3,4,5,6,12,13,14,15}. The remaining possible numbers are still in order and the gap is irrelevant.

So there is really no difference between this game and playing the higher/lower game. The best you are assured of is ruling out half the possibilities (rounded down) with each guess.

Posted by Jer on 2019-10-26 13:59:23

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