We decide to play the following game: An integer N will be randomly selected from the interval 0 - 100, inclusive. You try to guess N. After each guess, I tell you whether N is higher or lower than your guess.

If you successfully guess the integer, you win N dollars. Each guess costs you K dollars.

For each of the variants (a) and (b) below, what is the maximum value of K for which you'd be willing to play this game? Which strategy would you use to try to maximize your winnings in the long run?

(a) Once you start a round, you must continue until you guess N exactly.

(b) You may stop playing a round if you determine that N is too small to keep paying more money to guess N exactly. The money you've already spent on guesses is lost, but you may then start a new round with a new N.

(In reply to Part a (pencil and paper spoiler) by Steve Herman)

 A point above the midpoint makes more sense

so does a point BELOW the midpoint.

EXACTLY THE SAME - due to symmetry- just map mp+1 into mp-1.

Posted by Ady TZIDON on 2014-05-17 03:39:07