Ponder This

June 2007

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Ponder This Challenge:

You are playing a game in which you can ask for numbers. Each such number is a random value uniformly (and independently) distributed between 0 and 1. After you receive each number you can decide whether to request an additional number or to stop. When you stop your score is the sum of all the numbers you have received. Let 0<x<1. We ask two questions.

1. Suppose you are trying to achieve a score between x and 1. What are your chances of success?
2. Suppose you are trying to achieve a score between n+x and n+1. What are your chances of success in the limit as n --> infinity?

In both cases assume you are following the obvious best strategy. The answers are simple functions of x. Both questions must be answered correctly for credit.

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

  

Challenge: 06/01/2007 @ 05:00 PM EDT
Solution: 07/06/2007 @ 02:30 PM EDT
List Updated: 07/11/2007 @ 01:15 PM EDT

People who answered correctly:

Henry Bottomly (06.01.2007 @11:24:32 PM EDT)
Michael Brand (06.02.2007 @06:18:49 AM EDT)
Roberto Tauraso (06.02.2007 @10:09:37 AM EDT)
Frank Yang (06.02.2007 @12:28:16 PM EDT)
John T. Robinson (06.02.2007 @03:20:44 PM EDT)
V Balakrishnan (06.02.2007 @09:49:02 PM EDT)
Gary Gerken (06.02.2007 @11:53:12 PM EDT)
Christian Blatter (06.03.2007 @09:20:09 AM EDT)
Celia Anteneodo (06.03.2007 @07:59:04 PM EDT)
Renato Fonseca (06.03.2007 @10:13:16 PM EDT)
Ashish Srivastava (06.03.2007 @11:22:41 PM EDT)
James Dow Allen (06.04.2007 @02:14:25 AM EDT)
Andreas Eisele (06.04.2007 @05:44:34 AM EDT)
Eugene Vasilchenko (06.04.2007 @01:16:35 PM EDT)
Dan Dima (06.04.2007 @04:14:11 PM EDT)
Arthur Breitman (06.04.2007 @07:46:19 PM EDT)
Ed Sheppard (06.04.2007 @10:22:43 PM EDT)
Zhou Guang (06.04.2007 @10:48:17 PM EDT)
Heiko Selber (06.05.2007 @11:13:58 AM EDT)
John Tromp (06.05.2007 @12:13:33 PM EDT)
Luke Pebody (06.05.2007 @04:19:19 PM EDT)
David Friedman (06.07.2007 @02:25:28 PM EDT)
Ashish Mishra (06.06.2007 @03:27:33 PM EDT)
Alan Murray (06.06.2007 @09:46:54 PM EDT)
Murray Garth (06.07.2007 @06:46:57 AM EDT)
Mark Thornquist (06.07.2007 @06:13:52 PM EDT)
Wei Zhou (06.07.2007 @07:31:27 PM EDT)
Jiri Navratil (06.08.2007 @03:26:23 AM EDT)
Ashutosh Mehra (06.09.2007 @03:33:27 AM EDT)
Bart De Vylder (06.11.2007 @10:14:45 AM EDT)
Nancy Schechner (06.11.2007 @03:27:35 PM EDT)
suthambhara (06.13.2007 @12:16:50 AM EDT)
Rick Kaye (06.13.2007 @02:46:14 PM EDT)
Joseph C. Bonneau (06.14.2007 @11:49:18 AM EDT)
Gale W. Greenlee (06.14.2007 @12:16:22 PM EDT)
Erik Hostens (06.15.2007 @04:34:33 AM EDT)
John Fletcher (06.16.2007 @06:58:40 PM EDT)
David McQuillan (06.17.2007 @05:45:38 AM EDT)
William C. Hasenplaugh (06.17.2007 @06:25:16 PM EDT)
Dion Harmon (06.18.2007 @03:10:53 PM EDT)
Ji Feng (06.18.2007 @04:01:07 PM EDT)
Phil Muhm (06.19.2007 @09:16:12 AM EDT)
Ariel Flat (06.23.2007 @11:16:26 AM EDT)
Chris Shannon (06.26.2007 @01:18:21 AM EDT)
Chris Danielian (06.27.2007 @02:39:45 PM EDT)
Maxim Smith (06.27.2007 @03:22:10 PM EDT)
Majid Khabbazian (06.29.2007 @12:55:38 AM EDT)
Andrea Andenna (06.29.2007 @07:08:28 PM EDT)
Dharmadeep Muppalla (06.29.2007 @11:53:25 PM EDT)
Ilya Khivrich (06.30.2007 @12:27:54 PM EDT)
Arun Sivaramakrishnan (06.30.2007 @01:15:37 PM EDT)
Adriano Batista (06.30.2007 @09:48:05 PM EDT)
Du Yang (07.02.2007 @12:25:28 AM EDT)
Se Kwon Kim (07.04.2007 @11:55:52 AM EDT)

Attention: If your name is posted here and you wish it removed please send email to the ponder@il.ibm.com.