You are trying to guess my favorite number. I tell you it is from 1100 somewhere and is an interger. You can guess anything you like and I will tell you whether my number is higher or lower then your guess. What is the smallest number of guesses you can make to make sure you will get my number, no matter what it is?
Assume that I don't lie to you about the greater or less than value.
(In reply to
Is this right? by Gamer)
Even if you know the number after 6 guesses with a binary system, you "trying to guess [Jon's] favorite number," as stated in the introduction. Therefore, it will take an extra guess, and the fewest number you can do it in is seven.
The problem states, "You can guess anything you like and I will tell you whether my number is higher or lower then (sic) your guess."
Regarding the range, let's use the example you suggested. I guess that the number is between 82 and 90. Jon does not then have to say, "That's it!" Similarly, he will not say "Both," as the number is neither higher nor lower than my guess (not both). I am guessing a range, not two values.
Rather, he will say if it is higher or lower, or if the number is indeed in that range, he will either say nothing or say that the number is not higher or lower than my guess.
Thus, I think that it will work as I described, and you can find (and guess) the number with six guesses.
A final minor point, I don't think that every problem in which the solution is not obvious is required to be categorized under 'Tricks."

Posted by DJ
on 20030619 16:53:58 