IBM Research | Ponder This | April 2007 challenges

# Ponder This

## April 2007

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Ponder This Challenge:

This month's puzzle concerns a frog who is hopping on the integers from minus infinity to plus infinity. Each hop is chosen at random (with equal probability) to be either +2 or -1. So the frog will make steady but irregular progress in the positive direction. The frog will hit some integers more than once and miss others entirely. What fraction of the integers will the frog miss entirely? Please find an exact answer.

Update, 4/20/07: You may consider the answer to be the limit as N goes to infinity of the fraction of integers between -N and N a frog starting at -N and randomly hopping as described misses on average. Also an answer correct to six decimal places is good enough.

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Challenge: 04/04/2007 @ 11:00 AM EDT
Solution: 05/01/2007 @ 10:00 AM EDT
List Updated: 05/02/2007 @ 11:30 AM EDT

V Balakrishnan (04.04.2007 @02:22:47 PM EDT)
Frank Yang (04.05.2007 @10:35:20 AM EDT)
Michael Quist (04.05.2007 @11:08:35 AM EDT)
Alan Murray (04.05.2007 @12:54:18 PM EDT)
Dan Dima (04.05.2007 @02:31:45 PM EDT)
Dion Harmon (04.05.2007 @04:17:21 PM EDT)
Mark Perkins (04.05.2007 @06:23:28 PM EDT)
Joseph DeVincentis (04.05.2007 @09:57:57 PM EDT)
Tom Gutman (04.06.2007 @03:06:13 AM EDT)
ariel flat (04.06.2007 @07:54:11 PM EDT)
John T. Robinson (04.07.2007 @12:43:06 AM EDT)
Ed Sheppard (04.07.2007 @02:29:28 AM EDT)
zhou guang (04.09.2007 @01:11:50 AM EDT)
David McQuillan (04.10.2007 @02:29:08 PM EDT)
John G. Fletcher (04.11.2007 @10:50:51 PM EDT)
Celia Anteneodo (04.11.2007 @11:15:18 PM EDT)
Chris Danielian (04.12.2007 @06:13:32 PM EDT)
Christian Blatter (04.13.2007 @05:44:06 AM EDT)
Gale Greenlee (04.13.2007 @03:49:20 PM EDT)
Koen Vossen (04.15.2007 @06:39:55 PM EDT)
Ashish Srivastava (04.18.2007 @05:01:22 PM EDT)
Ron Yu (04.18.2007 @08:13:01 PM EDT)
Nyles Heise (04.19.2007 @02:27:09 AM EDT)
Renato Fonseca (04.19.2007 @09:31:20 PM EDT)
Yurun Liu (04.21.2007 @12:33:42 PM EDT)
Rob Berger (04.22.2007 @02:35:48 PM EDT)
Xianchao Xie (04:23:2007 @09:47:35 AM EDT)
Mark Thornquist (04.23.2007 @07:53:56 PM EDT)
Marcus Hedbring (04.24.2007 @10:02:48 AM EDT)
Teodora Baeva (04.24.2007 @03:14:43 PM EDT)
Adel El-Atawy (04.25.2007 @06:17:16 PM EDT)
Roberto Tauraso (04.26.2007 @04:15:46 PM EDT)
Wolf Mosle (04.27.2007 @05:08:13 PM EDT)
Andreas Eisele (04.27.2007 @05:55:33 PM EDT)
Dharmadeep Muppalla (04.28.2007 @06:40:47 AM EDT)
Paulo Sousa (04.29.2007 @10:01:27 AM EDT)
Pedro Fonseca (04.29.2007 @10:13:46 AM EDT)
Jiri Navratil (04.30.2007 @02:42:54 AM EDT)
Phil Muhm (04.30.2007 @03:38:26 PM EDT)
Hsiu-Khuern Tang (04.30.2007 @09:03:26 PM EDT)

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