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Guessing Game (Posted on 2014-05-16) Difficulty: 3 of 5
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.

No Solution Yet Submitted by tomarken    
Rating: 5.0000 (1 votes)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re(5): Additional thoughtsSteve Herman2014-05-21 16:43:31
Some Thoughtsre(4): Additional thoughtstomarken2014-05-21 12:52:15
re(3): Additional thoughtsSteve Herman2014-05-21 02:16:23
Hints/Tipsre(2): Additional thoughtstomarken2014-05-20 09:50:53
re: Additional thoughtsBrian Smith2014-05-19 07:34:34
Additional thoughtsSteve Herman2014-05-18 14:19:56
Some Thoughtsrational play for the highest integral K allowing play in part bCharlie2014-05-18 13:16:04
SolutionRepaired VB program agrees with Steve's answer to part bCharlie2014-05-18 12:06:44
re(3): different part b solution (VB program)Charlie2014-05-18 01:13:25
re(2): different part b solution (VB program)Steve Herman2014-05-17 17:08:23
re: different part b solution (VB program)Charlie2014-05-17 16:43:29
Solutiondifferent part b solution (VB program)Charlie2014-05-17 16:15:35
Part b solution (spoiler)Steve Herman2014-05-17 15:23:09
Part b strategy and methodology (a start)Steve Herman2014-05-17 14:30:21
Hints/Tipsre: Part a (pencil and paper spoiler)Ady TZIDON2014-05-17 03:39:07
SolutionPart a (pencil and paper spoiler)Steve Herman2014-05-17 02:32:55
Solutionpart a solutionCharlie2014-05-17 01:35:39
Ideas for part (a)Jer2014-05-16 16:04:57
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