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Interval Guessing (Posted on 2019-10-21) Difficulty: 2 of 5
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: some thoughts -- cases of small n | Comment 3 of 10 |
(In reply to some thoughts by Steven Lord)

If n=4, choosing first 1-2 and then individual halves (the binary method), gives a probability of 1/2 of hitting the number on try 2 and 1/2 on trial 3 for an expected value of 5/2 = 2.5.

Choosing individual numbers in turn gives 1/4 of finding on any given try for an expected value of 10/4 = 2.5.

What about n=3? Individual numbers gives expected value 6/3 = 2. The binary method, if using the floor of half the remaining number as the size of the next guess is actually the same as the individual member method.

  Posted by Charlie on 2019-10-23 13:37:56
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