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Ponder This

June 2011

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Ponder This Challenge:

The winner of the IBM Global Entrepreneur of the Year contest for 2010 was Streetline (see here details and a great six-minute pitch on their innovative parking system), so we decided to focus this month's challenge on parking.

This challenge is based on a puzzle we heard from Yaniv Shmueli, who heard it himself a few years ago.

Let's assume that cars have a length of two units and that they are parked along the circumference of a circle whose length is 100 units, which is marked as 100 segments, each one exactly one unit long.

A car can park on any two adjacent free segments (i.e., it does not need any extra maneuvering space).

Our question is as follows: Let's assume that we start with an empty circle. We add one car at a time, and each car parks in a random free space (aligned to a unit length), till no such place exists. What is the expected number of cars that can park along that 100-unit-long circle?


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: 06/01/2011 @ 10:00 AM EST
Solution: 06/01/2011 @ 10:00 AM EST
List Updated: 06/01/2011 @ 10:00 AM EST

People who answered correctly:

Dan Dima (05/31/2011 03:21 PM EDT)
Chase Albert (05/31/2011 03:34 PM EDT)
David Friedman (05/31/2011 04:22 PM EDT)
Bill Baker (05/31/2011 05:30 PM EDT)
Bryan Wolf (05/31/2011 05:32 PM EDT)
Jon Evans (05/31/2011 05:39 PM EDT)
John T. Robinson (05/31/2011 06:04 PM EDT)
Matt Dobrin (05/31/2011 06:31 PM EDT)
Mark Perkins (05/31/2011 08:34 PM EDT)
Shilei Zang (05/31/2011 09:48 PM EDT)
Leif Jensen (06/01/2011 01:03 AM EDT)
Andrea Andenna (06/01/2011 01:03 AM EDT)
Jonathan Campbell (06/01/2011 02:56 AM EDT)
Ted Hench (06/01/2011 03:21 AM EDT)
Bi Suzhi (06/01/2011 03:43 AM EDT)
Utkarsh Upadhyay (06/01/2011 07:32 AM EDT)
Florian Fischer (06/01/2011 09:49 AM EDT)
Arthur Breitman (06/01/2011 11:12 AM EDT)
Vladimir Sedach (06/01/2011 11:46 AM EDT)
Daniel Zev (06/01/2011 12:09 AM EDT)
Nick Vigo & Kipp Johnson (06/01/2011 12:15 PM EDT)
Eric R. Farmer (06/01/2011 12:43 PM EDT)
Donald T. Dodson (06/01/2011 01:23 PM EDT)
Joseph DeVincentis (06/01/2011 01:43 PM EDT)
Jochen Voß (06/01/2011 02:21 PM EDT)
Danny Leshem (06/01/2011 03:06 PM EDT)
John Tromp (06/01/2011 03:48 PM EDT)
Álvaro Begué (06/01/2011 04:31 PM EDT)
Hamidreza Bidar (06/01/2011 05:48 PM EDT)
Vignesh Sethuraman (06/01/2011 08:55 PM EDT)
Harald van Dijk (06/01/2011 09:43 PM EDT)
Phil Benamy (06/01/2011 10:00 PM EDT)
Jing-yu Cui (06/01/2011 11:25 PM EDT)
Brian Bitto (06/02/2011 12:26 AM EDT)
James Dow Allen (06/02/2011 01:27 AM EDT)
Piet Orye (06/02/2011 05:11 AM EDT)
Alex Krusz (06/02/2011 06:19 AM EDT)
Donald Laackman (06/02/2011 06:45 AM EDT)
Jan Fricke (06/02/2011 07:36 AM EDT)
Chen Wei (06/02/2011 09:09 AM EDT)
Christian Blatter (06/02/2011 09:15 AM EDT)
Bob Frank (06/02/2011 09:45 AM EDT)
Josh Small (06/02/2011 09:58 AM EDT)
Ariel Landau (06/02/2011 05:33 PM EDT)
Jörg Härterich (06/02/2011 06:47 PM EDT)
Ernest Zeidman (06/02/2011 07:33 PM EDT)
Austin Shapiro (06/02/2011 08:54 PM EDT)
Alex Krusz (06/03/2011 03:46 AM EDT)
aman_cc (06/03/2011 06:10 AM EDT)
Pengyu Chen (06/03/2011 11:01 AM EDT)
Owen Wright (06/03/2011 05:01 PM EDT)
Wenxun Huang (06/03/2011 08:28 PM EDT)
Sriram Sankaranarayanan (06/03/2011 08:51 PM EDT)
Nick McGrath (06/04/2011 01:00 AM EDT)
Clive Tong (06/04/2011 01:08 PM EDT)
Motty Porat (06/04/2011 04:50 PM EDT)
Karthik Kalyanam (06/04/2011 05:08 PM EDT)
Jason Crease (06/04/2011 05:29 PM EDT)
Sylvain Becker (06/04/2011 05:51 PM EDT)
Anthony Helmstetter (06/04/2011 06:39 PM EDT)
Siddharth S (06/05/2011 03:58 AM EDT)
Amos Guler (06/05/2011 03:59 AM EDT)
Vijay Comsci (06/05/2011 05:02 AM EDT)
Or Zuk (06/05/2011 09:31 AM EDT)
Thijmen Krebs (06/05/2011 04:29 PM EDT)
Mark Mixer (06/05/2011 04:51 PM EDT)
Sergei Agievich (06/05/2011 06:24 PM EDT)
Blacklight (06/05/2011 11:20 PM EDT)
Robert C. Sarvis (06/05/2011 11:41 PM EDT)
Maris Van Sprang (06/06/2011 04:45 AM EDT)
Lu Wang (06/06/2011 11:51 AM EDT)
Daniel Bitin (06/06/2011 01:59 PM EDT)
Ryan Manuel (06/06/2011 04:46 PM EDT)
Ian Smith (06/06/2011 05:55 PM EDT)
Joseph Bonneau (06/06/2011 07:40 PM EDT)
Jon Namnath (06/06/2011 08:35 PM EDT)
John Snyder (06/06/2011 11:59 PM EDT)
Kiyoto Tamura (06/07/2011 01:21 AM EDT)
Michael Brand (06/07/2011 0600 AM EDT)
John Schanck (06/07/2011 04:28 PM EDT)
Teemu Stenhammar (06/07/2011 05:28 PM EDT)
Joe Riel (06/07/2011 09:09 PM EDT)
Liubing Yu (06/08/2011 06:08 AM EDT)
Mehmet Sariyuce & Umut Uludag (06/08/2011 09:00 AM EDT)
George Savvas (06/09/2011 12:12 AM EDT)
William Heller (06/09/2011 01:48 AM EDT)
Serge Thill (06/09/2011 11:53 AM EDT)
Evert van Dijken (06/10/2011 04:24 AM EDT)
Guoxin Zhang (06/10/2011 01:33 PM EDT)
Balakrishnan V (06/11/2011 03:21 PM EDT)
Jeff Steele (06/11/2011 08:02 PM EDT)
Anoop Ghanwani (06/12/2011 03:27 AM EDT)
Joseph Calzaretta (06/12/2011 10:14 PM EDT)
Yaniv Meoded (06/13/2011 06:12 AM EDT)
Sandeep Rathour (06/13/2011 08:31 AM EDT)
Miss Shawn Simpson (06/13/2011 02:11 PM EDT)
Algirdas Rašcius (06/13/2011 05:39 PM EDT)
Miguel Cuartas Hernández (06/15/2011 03:59 AM EDT)
Joseph Manger (06/16/2011 08:28 AM EDT)
Jonathan Fader (06/16/2011 10:46 AM EDT)
Ariel Flat (06/16/2011 01:45 PM EDT)
Sam Vercauteren (06/16/2011 09:06 PM EDT)
Chris Hills (06/16/2011 09:17 PM EDT)
John G Fletcher (06/17/2011 01:52 AM EDT)
Kaverappa O T (06/17/2011 06:09 AM EDT)
Daniel Jaouen (06/19/2011 03:14 AM EDT)
Gale Greenlee (06/20/2011 01:10 PM EDT)
Ilya Khivrich (06/20/2011 06:29 PM EDT)
Andrew Buchanan (06/21/2011 02:31 PM EDT)
Charles Ward (06/22/2011 02:08 PM EDT)
Soumitra Pal (06/22/2011 03:59 AM EDT)
Yifei Wu (06/22/2011 04:36 PM EDT)
Reiner Martin (06/24/2011 06:25 AM EDT)
Daniel Camero (06/24/2011 11:16 AM EDT)
Gil Dollberg (06/24/2011 04:35 PM EDT)
Ante Kovacic (06/24/2011 06:25 PM EDT)
Frederik Kaster (06/25/2011 11:33 AM EDT)
Yuyuan Ouyang (06/25/2011 04:09 PM EDT)
Taher Jamshidi (06/26/2011 12:10 PM EDT)
Li Xu (06/27/2011 05:43 AM EDT)
Ashray Urs (06/27/2011 03:19 PM EDT)
Mauro Bampo (06/28/2011 02:26 AM EDT)
Albert Stadler (06/28/2011 12:52 PM EDT)
Rob Pratt (06/28/2011 05:48 PM EDT)
Chris Shannon (06/28/2011 08:33 PM EDT)
Robert Buckley (06/29/2011 01:13 PM EDT)
Jintao Yin (06/30/2011 02:31 AM EDT)
David Tam (06/30/2011 02:53 AM EDT)
Franza Cavalcante Jr (06/30/2011 06:20 PM EDT)
Rogerio Ponce da Silva (07/01/2011 05:04 AM EDT)
Hakan Summakoglu (07/01/2011 03:17 PM EDT)
Ehud Schreiber (07/03/2011 09:05 AM EDT)
Aviv Nisgav (07/06/2011 06:24 AM EDT)


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