IBM Research | Ponder This | March 2007 challenges
Skip to main content

Ponder This

March 2007

<<February March April>>

Ponder This Challenge:

Puzzle for March 2007.

This month's puzzle is about a two player game involving a shooter, S, and a target, T. The target can move among three locations 0,1,2. The game is played in rounds. Each round begins with T located where he was at the conclusion of the previous round. In each round T can choose to stay at the same location or move to a location 1 different. So T can move freely among the locations except moves from 0 to 2 or 2 to 0 are impossible. In each round S also picks a location (without knowing the T's choice). If T and S pick the same location S scores a point. At the end of each round S is told T's new location. The game is played over many rounds.

Part 1: The objective of S is to score points at the greatest possible rate. The objective of T is to allow S to score points at the least possible rate. If S and T play optimally at what rate (points/round) will S score points?

Part 2: Suppose the objectives are reversed, T is trying to get S to score points and S is trying to avoid scoring points. Again if both play optimally at what rate will S score?

**Note: a correct solution is required for both parts.

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

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


Challenge: 03/02/2007 @ 4:30 PM EST
Solution: 04/04/2007 @ 11:00 AM EDT
List Updated: 04/11/2007 @ 10:50 AM EDT

People who answered correctly:

Michael Brand (03.02.2007 @07:07:24 PM EST)
Tom Gutman (03.02.2007 @07:22:29 PM EST)
Alan Murray (03.03.2007 @12:54:32 PM EST)
Ed Shepard (03.03.2007 @11:06:16 PM EST)
James Dow Allen (03.03.2007 @11:22:26 PM EST)
Bart De Vylder (03.04.2007 @ 07:11:15 AM EST)
Yoav Raz (03.04.2007 @10:08:32 PM EST)
Antonio Manuel Gutierrez Fernandez (03.05.2007 @12:15:57 PM EST)
Luke Pebody (03.05.2007 @06:29:25 PM EST)
Frank Yang (03.05.2007 @10:14:49 PM EST)
Joseph DiVincentis (03.05.2007 @10:51:58 PM EST)
Serge Gautier (03.06.2007 @08:06:37 AM EST)
Gale Greenlee (03.06.2007 @10:50:33 AM EST)
John T. Robinson (03.06.2007 @04:57:24 PM EST)
Joshua Green (03.06.2007 @05:31:38 PM EST)
Dan Dima (03.06.2007 @06:39:39 PM EST)
Dharmadeep Muppalla (03.06.2007 @11:22:58 PM EST)
Gary M Gerken (03.07.2007 @12:03:03 AM EST)
Wolf Mosle (03.07.2007 @01:53:37 PM EST)
V Balakrishnan (03.07.2007 @02:30:28 PM EST)
Celia Anteneodo (03.07.2007 @07:54:27 PM EST)
Patrick J. LoPresti (03.08.2007 @02:02:23 AM EST)
Ashish Srivastav (03.09.2007 @03:14:39 AM EST)
Greg Janee (03.09.2007 @12:52:03 PM EST)
Andrew Buchanan (03.10.2007 @04:54:16 AM EST)
Arjun Acharya (03.10.2007 @08:55:59 PM EST)
Adriano Batista (03.11.2007 @10:54:22 PM EDT)
Zhou Guang (03.12.2007 @03:56:47 AM EDT)
arnab.x.bose (03.12.2007 @10:20:37 AM EDT)
Kerry M. Soileau (03.12.2007 @ 03:45:00 PM EDT)
Forrest McClellan (03.13.2007 @05:03:07 PM EDT)
Andrea Andenna (03.14.2007 @01:09:52 PM EDT)
Clive Tong (03.14.2007 @05:28:51 PM EDT)
Se Kwon Kim (03.16.2007 @10:11:23 PM EDT)
Dion Harmon (03.20.2007 @03:50:20 PM EDT)
David McQuillan (03.21.2007 @07:08:41 PM EDT)
Jiri Navratil (03.22.2007 @06:30:26 PM EDT)
Teodora Baeva (03.24.2007 @o5:25:25 PM EDT)
Mark Pilloff (03.27.2007 @08:32:27 PM EDT)
Alan Curry (03.28.2007 @07:35:22 PM EDT)
Phil Muhm (03.30.2007 @12:08:24 PM EDT)
Du Yang (03.31.2007 @09:43:24 PM EDT)
Rogerio Ponce da Silva (04.01.2007 @07:47:31 PM EDT)
Koen Vossen (04.03.2007 @06:18:02 PM EDT)

Attention: If your name is posted here and you wish it removed please send email to the