IBM Research | Ponder This | January 2008 challenges

# Ponder This

## January 2008

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Ponder This Challenge:

This month's puzzle concerns drawing balls from an urn. You know the urn contains 3 balls. You know each ball is white or black and that white balls are worth 1 unit, black balls are worth nothing. You know the urn is equally likely to contain 0,1,2 or 3 white balls. You have an opportunity to buy balls from the urn. Each ball costs c units (0<c<1). When you buy a ball one of the remaining balls in the urn is randomly selected and given to you. You may stop buying balls at any time based on the color of the balls you have received. Assuming you adopt the best strategy, what is your expected return as a function of c?

UPDATE, 1/3/08: You do not have to buy any balls. By return I mean the value of the balls you receive minus their cost.

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: 01/02/2008 @ 01:30 AM EDT
Solution: 02/01/2008 @ 05:30 AM EDT
List Updated: 02/05/2008 @ 11:30 AM EDT

Ryan Milligan (01.02.2008 @05:30:00 AM EST)
Andreas Eisele (01.02.2008 @05:30:06 AM EST)
V. Balakrishnan (01.02.2008 @08:58:53 AM EST)
Dan Dima (01.02.2008 @09:34:17 AM EST)
Luke Pebody (01.02.2008 @11:17:30 AM EST)
Frank Yang (01.02.2008 @12:42:14 PM EST)
Fred Batty (01.02.2008 @01:13:01 PM EST)
Jimmy Hu (01.02.2008 @04:28:20 PM EST)
Eugene Vasilchenko (01.02.2008 @04:52:27 PM EST)
Mark Perkins (01.02.2008 @05:23:19 PM EST)
John Tromp (01.02.2008 @05:24:32 PM EST)
Christian Blatter (01.03.2008 @05:30:49 AM EST)
Karl Morton (01.03.2008 @12:01:03 PM EST)
William C. Hasenplaugh (01.03.2008 @12:23:56 PM EST)
Joe Fendel (01.03.2008 @01:06:56 PM EST)
Erik Hostens (01.03.2008 @01:21:58 PM EST)
Mehmet Soyturk (01.03.2008 @05:42:38 PM EST)
Kai Guttmann (01.03.2008 @06:20:17 PM EST)
Joshua Green (01.03.2008 @10:44:42 PM EST)
John Ritson (01.03.2008 @11:03:30 PM EST)
Hongcheng Zhu (01.04.2008 @03:24:16 AM EST)
Dharmadeep Muppalla (01.04.2008 @09:33:11 AM EST)
Maxim G. Smith (01.04.2008 @11:04:42 AM EST)
James Dow Allen (01.04.2008 @01:36:55 PM EST)
Henry Bottomley (01.04.2008 @01:40:35 PM EST)
Dion Harmon (01.04.2008 @05:46:52 PM EST)
Gary M. Gerken (01.05.2008 @07:38:04 AM EST)
Matt Hickford (01.05.2008 @09:45:15 AM EST)
Al Zimmermann (01.05.2008 @10:38:43 AM EST)
Christie Marr (01.05.2008 @12:57:25 PM EST)
Joseph DeVincentis (01.05.2008 @01:06:11 PM EST)
Alan Murray (01.05.2008 @04:30:20 PM EST)
Mithil Ramteke (01.06.2008 @01:56:58 PM EST)
Jan Musschoot (01.06.2008 @04:03:30 PM EST)
Ed Shepard (01.06.2008 @08:06:09 PM EST)
Jochen Hoenicke (01.07.2008 @11:25:09 AM EST)
Samantha Casanova (01.07.2008 @01:53:59 PM EST)
Ashish Srivasta (01.07.2008 @04:06:02 PM EST)
Jiri Navratil (01.07.2008 @06:27:13 PM EST)
Anneke Van Steirteghem (01.08.2008 @10:52:07 AM EST)
Slawomir Pudlis (01.08.2008 @11:28:53 AM EST)
Victor Chang (01.08.2008 @02:34:21 PM EST)
zhouguang (01.08.2008 @10:14:20 PM EST)
Chris Lomont (01.09.2008 @09:06:46 AM EST)
Greg Jane (01.09.2008 @01:24:31 PM EST)
Chris Hills (01.09.2008 @05:28:55 PM EST)
Phil Muhm (01.09.2008 @10:41:58 PM EST)
Rubén Hernández Aza (01.09.2008 @10:52:04 PM EST)
John T. Robinson (01.10.2008 @12:34:40 PM EST)
Guillermo Ruiz (01.11.2008 @07:13:33 AM EST)
Andrea Andenna (01.13.2008 @09:55:10 AM EST)
Ole Martin (01.13.2008 @12:12:58 PM EST)
Øyvind Grotmol (01.13.2008 @04:21:40 PM EST)
Ian Smith (01.14.2008 @07:30:57 AM EST)
Mark Thornquist (01.15.2008 @06:47:20 PM EST)
Don Dodson (01.16.2008 @04:50:58 PM EST)
John Stebbins (01.18.2008 @01:25:02 AM EST)
Peter Chikov (01.18.2008 @11:56:21 AM EST)
Stephen Merriman (01.18.2008 @08:29:50 PM EST)
Aleksandar Damnjanovic (01.19.2008 @02:58:51 AM EST)
Amos Guler (01.20.2008 @03:15:42 AM EST)
John G. Fletcher (01.20.2008 @04:10:41 PM EST)
Nathaniel Litton (01.22.2008 @12:33:37 PM EST)
Volkmar Kobelt (01.23.2008 @10:09:30 AM EST)
Nyles Heise (01.24.2008 @03:04:44 AM EST)
Amit Sinha (01.26.2008 @05:31:41 PM EST)
Chuck Carroll (01.27.2008 @10:35:21 AM EST)
Arjun R. Acharya (01.27.2008 @07:10:26 PM EST)
Deepak (01.28.2008 @11:39:07 AM EST)
Gale Greenlee (01.28.2008 @11:41:13 AM EST)
Ashutosh Mahajan (01.28.2008 @01:57:05 PM EST)
Wolf Mosle (01.28.2008 @03:42:02 PM EST)
David Friedman (01.29.2008 @05:19:03 PM EST)
Thomas Hähndel (01.29.2008 @07:25:50 PM EST)
Chris Shannon (01.30.2008 @05:51:37 PM EST)
Albert Stadler (01.31.2008 @01:59:57 PM EST)
Michael Liepelt (01.31.2008 @02:51:38 PM EST)
Danny Walters (02.01.2008 @01:50:51 AM EST)

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