IBM Research | Ponder This | October 2002 challenges

# Ponder This

## October 2002

<<September October November>>

Ponder This Challenge:

This month's problem was sent in by Sudipta Das from Calcutta:

In a certain tournament, N players have been numbered 1 through N.
But, only M players can play the game together (1<M<N).
So, Players 1 through M start the game.
One of them goes out, and Player (M+1) joins the game.
This continues until there is no one left to join the game.

As a function of N and M, what is the probability that the game ended with an even-numbered player going out?

Closed-form solution is preferred (expressed without sums or recursion).

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: 10/01/2002 @ 03:00 PM EST
Solution: 10/31/2002 @ 10:00 AM EST
List Updated: 10/01/2002 @ 03:00 PM EST

Kunal Shroff (10.02.2002@02:36:15AM EDT)

Nancy Zvi (10.02.2002@09:13:12AM EDT)
Michael Brand (10.02.2002@10:15:21AM EDT)
Jonathan A. Wildstrom (10.02.2002@12:14:45PM EDT)
Hazem D. Elmeleegy (10.03.2002@06:07:06AM EDT)
Wu Zheng (10.03.2002@01:23:43PM EDT)
John G. Fletcher (10.03.2002@05:51:54PM EDT)
Manish Tayal (10.03.2002@06:23:49PM EDT)
Christie Bolton (10.04.2002@02:01:54PM EDT)
Gyora Benedek (10.06.2002@09:36:37AM EDT)
Hassan Masum (10.06.2002@07:13:47PM EDT)
Soonho You (10.07.2002@09:32:00PM EDT)
Joseph DeVincentis (10.07.2002@10:15:48PM EDT)
Chris Shannon (10.08.2002@01:47:29AM EDT)
Michael Swart (10.08.2002@09:33:50AM EDT)
Christopher Howe (10.08.2002@10:29:38AM EDT)
Francis Golding (10.08.2002@05:52:49PM EDT)
Ashish Mishra (10.08.2002@09:56:53PM EDT)
Karl Dsouza (10.08.2002@12:08:06PM EDT)
Kennedy (10.09.2002@01:10:50AM EDT)
Yuvraj Singh Dhillon (10.09.2002@01:31:15PM EDT)
Utku Diril (10.10.2002@11:04:20AM EDT)
Bartolini Claudio (10.10.2002@01:16:10PM EDT)
Sriram Rallabhandi (10.10.2002@02:51:56PM EDT)
Jayavel Sounderpandian (10.12.2002@04:17:53AM EDT)
Sarang Aravamuthan (10.12.2002@12:01:35PM EDT)
L.T. Pebody (10.14.2002@05:36:59PM EDT)
Michael Lieberman (10.14.2002@10:47:34PM EDT)
Christopher Yao (10.18.2002@06:35:21PM EDT)
Cervenansky Peter (10.21.2002@11:08:58AM EDT)
Hagen von Eitzen (10.21.2002@01:45:32PM EDT)
Deepu Sebastian Joseph (10.21.2002@02:35:36PM EDT)
Maxim G. Smith (10.25.2002@02:53:11PM EDT)