IBM Research | Ponder This | March 2007 challenges

# Ponder This

## March 2007

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

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)

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