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Ponder This

December 2012

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Ponder This Challenge:

36 people live in a 6x6 grid, and each one of them lives in a separate square of the grid. Each resident's neighbors are those who live in the squares that have a common edge with that resident's square.

Each resident of the grid is assigned a natural number N, such that if a person receives some N>1, then he or she must also have neighbors that have been assigned all of the numbers 1,2,...,N-1.

Find a configuration of the 36 neighbors where the sum of their numbers is at least 90.

Finding a sum of 90+N will earn you N stars near your name.

As an example, the highest sum we can get in a 3x3 grid is 20:
1 2 1
4 3 4
2 1 2

An accompanying riddle, relating to a generalized version of this problem, appears in this month's Using your Head is Permitted
( http://www.brand.site.co.il/riddles/201212q.html).


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 webmaster.

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

  

Challenge: 29/11/2012 @ 01:00 PM EST
Solution: 02/01/2013 @ 01:00 PM EST
List Updated: 29/11/2012 @ 01:00 PM EST

People who answered correctly:

Robin Ryder (11/29/2012 03:48 PM EDT)
Zilin Jiang (11/29/2012 04:16 PM EDT)
Peter de Rivaz (11/29/2012 04:18 PM EDT)
***David Greer (11/29/2012 04:57 PM EDT)
***Deron Stewart (11/29/2012 05:07 PM EDT)
Chuck Carroll (11/29/2012 05:43 PM EDT)
*Todd Will (11/29/2012 05:40 PM EDT)
Mark Perkins (11/29/2012 06:16 PM EDT)
***Dan Dima (11/29/2012 06:40 PM EDT)
Deane Stewart (11/29/2012 07:01 PM EDT)
*Adrian Orzepowski (11/29/2012 07:30 PM EDT)
*Philip Cerles (11/29/2012 10:34 PM EDT)
*Kevin Sham (11/30/2012 01:07 AM EDT)
***Levent Erkok (11/30/2012 03:49 AM EDT)
**Anders Kaseorg (11/30/2012 04:29 AM EDT)
Kris Reyes (11/30/2012 06:13 AM EDT)
Jay R. Joshi (11/30/2012 09:29 AM EDT)
***Daniel Bitin (11/30/2012 09:50 AM EDT)
***Donald Dodson (11/30/2012 01:12 PM EDT)
Gergely Pataki (11/30/2012 01:51 PM EDT)
***Matej Kollar (11/30/2012 01:56 PM EDT)
*Zhichen Zhao (11/30/2012 04:45 PM EDT)
János Kramár (11/30/2012 05:00 PM EDT)
***Mark Mammel (11/30/2012 07:11 PM EDT)
Hamidreza Bidar (11/30/2012 07:21 PM EDT)
Chhavi Gupta (11/30/2012 07:42 PM EDT)
***Řyvind Grotmol (11/30/2012 08:12 PM EDT)
Pataki Gergely (11/30/2012 08:50 PM EDT)
**Florian Fischer (11/30/2012 09:05 PM EDT)
*James Hutchinson (11/30/2012 10:56 PM EDT)
***Tomek Czajka (12/01/2012 12:03 AM EDT)
Ashfaque Shaikh (12/01/2012 03:24 AM EDT)
*Tengyuan Liang (12/01/2012 04:44 AM EDT)
***Ben Andken (12/01/2012 01:16 PM EDT)
Tony Maric & Vicki Kysar (12/01/2012 01:48 PM EDT)
**Michael Davis (12/01/2012 02:06 PM EDT)
***Hakan Summakoglu (12/01/2012 02:14 PM EDT)
*James Dow Allen (12/01/2012 03:23 PM EDT)
**Mark Pervovskiy (12/01/2012 03:27 PM EDT)
***Siva Dirisala (12/01/2012 06:13 AM EDT)
Maris Van Sprang (12/01/2012 03:51 PM EDT)
Anant Sharma (12/01/2012 04:40 PM EDT)
Adam Kozdron (12/01/2012 05:46 PM EDT)
Joseph DeVincentis (12/01/2012 08:01 PM EDT)
***Aharon Malachi (12/01/2012 08:11 PM EDT)
**Andy Carle (12/01/2012 10:15 PM EDT)
***Guangda Huzhang (12/02/2012 01:31 AM EDT)
***Oleg Zlydenko (12/02/2012 03:34 AM EDT)
***Dennis Langdeau (12/02/2012 03:54 AM EDT)
***Danny Antonetti (12/02/2012 04:29 AM EDT)
***Andreas Razen & Radu-Alexandru Todor (12/02/2012 06:50 AM EDT)
Katarzyna Wojdziak (12/02/2012 01:47 PM EDT)
**Rahul Bartakke (12/02/2012 01:59 PM EDT)
*Tulasi Ram Reddy (12/02/2012 02:47 PM EDT)
*Aditya Utturwar (12/02/2012 03:36 PM EDT)
***Peter Gerritson (12/02/2012 04:14 PM EDT)
***Hubert Kahlert (12/02/2012 04:46 PM EDT)
***Alex Wagner (12/02/2012 05:06 PM EDT)
***Carlos Henrique Cardonha (12/02/2012 07:00 PM EDT)
*Lorenzo Gianferrari Pini (12/02/2012 08:51 PM EDT)
Philipp Horsch (12/02/2012 10:57 PM EDT)
*Hillel Lee Sing Chun (12/03/2012 04:35 AM EDT)
Ashish Kumar (12/03/2012 05:33 AM EDT)
*Jong Wook Kim (12/03/2012 08:51 AM EDT)
Nachiketa Kumar (12/03/2012 09:10 AM EDT)
Adrian Liebtrau (12/03/2012 10:29 AM EDT)
*Andreas Stahl (12/03/2012 12:34 PM EDT)
*Shengkai Cao (12/03/2012 12:48 PM EDT)
Latricia Golden (12/03/2012 01:37 PM EDT)
***Armin Krauss (12/03/2012 02:17 PM EDT)
**Yang Jiang (12/03/2012 02:28 PM EDT)
Tanja Artiga Gonzalez (12/03/2012 02:46 PM EDT)
**Jan Völkel (12/03/2012 04:04 PM EDT)
Simon Foster (12/03/2012 06:03 PM EDT)
Adam Daire (12/03/2012 07:05 PM EDT)
***Álvaro Begué (12/03/2012 07:56 PM EDT)
Gordon Burtch (12/03/2012 08:11 PM EDT)
***Rob Pratt (12/03/2012 09:13 PM EDT)
**Thomas Fleming (12/03/2012 09:51 PM EDT)
**Boaz Menuhin (12/03/2012 11:00 PM EDT)
Aaron Friedland (12/03/2012 10:53 PM EDT)
**Naftali Peles (12/04/2012 12:29 AM EDT)
**Liubing Yu (12/04/2012 12:41 AM EDT)
John Colby (12/04/2012 01:18 AM EDT)
***Andrew Rochon (12/04/2012 03:04 AM EDT)
Panagiotis Tsikogiannopoulos (12/04/2012 06:52 AM EDT)
*Ben Green (12/04/2012 07:13 AM EDT)
Harsha HS (12/04/2012 08:09 AM EDT)
Tobias Philipp (12/04/2012 11:57 AM EDT)
***Hugo Pfoertner (12/04/2012 01:20 PM EDT)
***Irv Lustig (12/04/2012 02:45 PM EDT)
Hannes Schenck (12/04/2012 04:02 PM EDT)
***Frederik Kaster (12/04/2012 04:01 PM EDT)
***Christopher E. Marks (12/04/2012 04:55 PM EDT)
*Aleksey Voroshilov (12/04/2012 05:30 PM EDT)
***Roddy Kok (12/04/2012 05:36 PM EDT)
***Landon Kryger (12/04/2012 07:08 PM EDT)
Greg Fritz (12/04/2012 08:26 PM EDT)
***Joe Clark (12/04/2012 08:30 PM EDT)
***Jamie Jorgensen & Jason Lee (12/04/2012 09:20 PM EDT)
Graham McHardy (12/04/2012 10:58 PM EDT)
**Andrzej Janiak (12/04/2012 11:20 PM EDT)
Matthew Wood (12/05/2012 12:09 AM EDT)
Shimaa Maher (12/05/2012 02:35 AM EDT)
***Janos Csorba (12/05/2012 08:40 AM EDT)
Gaurav Bajaj (12/05/2012 09:25 AM EDT)
***Kevin Bauer (12/05/2012 11:25 AM EDT)
Amita Sontakke (12/06/2012 12:43 AM EDT)
Cliff Haithcock (12/06/2012 03:50 AM EDT)
***Ofer Reichman (12/06/2012 05:50 AM EDT)
Luke Anklesaria (12/06/2012 06:16 AM EDT)
***Michael Liepelt (12/06/2012 06:33 AM EDT)
Piny Houri (12/06/2012 11:38 AM EDT)
***Chris Davey (12/06/2012 02:43 PM EDT)
Movin Jain (12/06/2012 03:28 PM EDT)
***Stéphane Higueret (12/06/2012 04:38 PM EDT)
*Rosanna Holdsworth (12/06/2012 05:23 PM EDT)
*Joel Baker (12/06/2012 10:37 PM EDT)
*Rastko Anicic (12/06/2012 11:28 PM EDT)
***Tony Harrison (12/07/2012 09:32 AM EDT)
Umut Uludag (12/07/2012 09:44 AM EDT)
*Jayakumar Hoskere (12/07/2012 12:57 PM EDT)
Simon Pratt (12/07/2012 02:27 PM EDT)
Adam Danger (12/07/2012 02:28 PM EDT)
***Michael Rosola (12/07/2012 06:18 PM EDT)
Spiegel Sanford (12/07/2012 07:18 PM EDT)
***Andrei Zaharescu (12/08/2012 12:32 AM EDT)
***Cong Zhao (12/08/2012 04:20 AM EDT)
***Greg Bubnis (12/08/2012 10:32 AM EDT)
Anil Purohit (12/08/2012 11:35 AM EDT)
Peter Steele (12/08/2012 01:13 PM EDT)
Luisma Frutos (12/08/2012 09:51 PM EDT)
*Dan Ignatoff (12/09/2012 04:55 AM EDT)
Arun Ramachandran (12/09/2012 10:23 AM EDT)
***Simin Cheng (12/09/2012 10:56 AM EDT)
***Andrei Zaharescu (12/10/2012 12:55 AM EDT)
Vibhakar Shukla (12/10/2012 11:54 AM EDT)
***Jason Crease (12/10/2012 12:27 PM EDT)
**Rony Joseph (12/10/2012 12:46 PM EDT)
***Serge Gautier (12/10/2012 03:04 PM EDT)
***Amos Guler (12/11/2012 05:07 AM EDT)
***Puvichakravarthy Ramachandran (12/11/2012 10:15 AM EDT)
**Nachiketa Kumar (12/11/2012 03:42 PM EDT)
***Levon Haykazyan (12/11/2012 03:54 PM EDT)
*Javier Rodriguez (12/11/2012 07:44 PM EDT)
Michael Chirozzi (12/11/2012 07:49 PM EDT)
Phil Benamy (12/12/2012 12:42 AM EDT)
***Sridivakar Inakonda (12/12/2012 03:23 AM EDT)
***Thomas Egense (12/12/2012 04:49 AM EDT)
***Cameron Stewart (12/12/2012 06:51 AM EDT)
**Srinivasan Iyer (12/12/2012 08:31 AM EDT)
***Lars Nagel (12/12/2012 11:31 AM EDT)
Mert Öztürk (12/12/2012 03:44 PM EDT)
**Sai Kulkarni (12/12/2012 05:10 PM EDT)
*Joachim Dörfer (12/12/2012 07:08 PM EDT)
Nachiket Bapat (12/12/2012 10:03 PM EDT)
Peter Armitage (12/12/2012 10:45 PM EDT)
***Michael D Moffitt (12/12/2012 11:54 PM EDT)
Victoria Krakovna (12/13/2012 01:16 AM EDT)
***Pablo Dal Lago (12/13/2012 04:43 AM EDT)
**Bartosz Budzanowski (12/13/2012 11:42 AM EDT)
*Nagendra Gulur Dwarakanath (12/13/2012 12:22 PM EDT)
Olivier Mercier (12/13/2012 04:15 PM EDT)
Ryan Ma (12/13/2012 05:50 PM EDT)
Sri Mallikarjun J (12/14/2012 01:32 AM EDT)
Brian Thomas (12/14/2012 04:18 AM EDT)
**Lewei Weng (12/14/2012 07:23 AM EDT)
Peter Park (12/14/2012 11:40 AM EDT)
Oliver Lau (12/14/2012 12:06 PM EDT)
*Nanmu (12/14/2012 02:41 PM EDT)
***Martin Husar (12/14/2012 03:56 PM EDT)
*Rajat Goyal (12/14/2012 06:40 PM EDT)
*Shi Jin (12/14/2012 07:30 PM EDT)
Peter Simonyi (12/14/2012 11:01 PM EDT)
***Ofer Reichman (12/15/2012 04:17 AM EDT)
**Edgardo Deza (12/15/2012 01:35 PM EDT)
***Mark Stuckel (12/16/2012 05:13 AM EDT)
**Will Buehler (12/16/2012 01:50 PM EDT)
**Alex Jeon (12/16/2012 07:26 PM EDT)
Neil Smeby (12/16/2012 11:12 PM EDT)
***Keith Amling (12/17/2012 02:08 AM EDT)
***Christian Pape (12/17/2012 08:53 AM EDT)
***Heiko Selber (12/17/2012 08:00 AM EDT)
*Waldek Zdanowicz (12/17/2012 01:08 PM EDT)
***Laurent Faureytier (12/17/2012 02:51 PM EDT)
Benjamin Raibaud (12/17/2012 06:21 PM EDT)
**David Friedman (12/15/2012 11:51 PM EDT)
***Harald Bögeholz (12/17/2012 09:25 PM EDT)
***Seth Troisi (12/17/2012 11:42 PM EDT)
***Shilei Zang (12/18/2012 02:01 AM EDT)
**Simon Foster (12/18/2012 08:37 AM EDT)
**Lucas Galfaso (12/18/2012 10:39 AM EDT)
***Halil Bayrak (12/18/2012 02:57 PM EDT)
***Johannes Waldmann (12/18/2012 04:58 PM EDT)
***John M Fonner (12/18/2012 05:52 PM EDT)
*Alex Zdanowicz (12/18/2012 07:41 PM EDT)
Gil Citro (12/18/2012 09:39 PM EDT)
*Adam Danger (12/18/2012 11:10 PM EDT)
**Seongwoo Hong (12/19/2012 01:19 PM EDT)
***Mark Pervovskiy (12/19/2012 03:48 PM EDT)
***Markus von Rimscha (12/19/2012 07:18 PM EDT)
Vitor Miguel (12/20/2012 03:31 PM EDT)
Geoff Kallweit (12/20/2012 03:58 PM EDT)
Maria Helena G. Costa (12/20/2012 05:33 PM EDT)
***Amit Bhatia (12/21/2012 06:17 AM EDT)
*Kipp Johnson (12/21/2012 12:18 AM EDT)
Ian Smith (12/21/2012 05:49 AM EDT)
***Pooja Keswani (12/21/2012 09:07 AM EDT)
***Joaquim Neves Carrapa (12/21/2012 09:53 AM EDT)
***Fabio Filatrella (12/21/2012 11:38 AM EDT)
***Joël Bleuse (12/22/2012 05:56 PM EDT)
Gueram Sargsyan (12/23/2012 10:46 AM EDT)
***Motty Porat (12/23/2012 05:34 PM EDT)
Troy Prario (12/23/2012 10:51 PM EDT)
***Rajendran Thirupugalsamy (12/24/2012 02:52 AM EDT)
**Aashay Harlalka (12/24/2012 05:41 AM EDT)
***Andreas Stiller (12/24/2012 08:31 AM EDT)
Paul Mandell (12/24/2012 10:35 AM EDT)
Nicholas Wegman (12/24/2012 02:42 PM EDT)
**Markus Boettle (12/24/2012 07:31 PM EDT)
*Andrey Stepin (12/25/2012 03:15 AM EDT)
***Geogry Chebanov (12/25/2012 02:55 PM EDT)
***Raman Khatri & Ankit Aggarwal (12/25/2012 06:55 PM EDT)
***Andrey Stepin (12/26/2012 12:30 AM EDT)
*Umang Mittal (12/27/2012 06:02 AM EDT)
Raghu Adari (12/27/2012 07:39 AM EDT)
***Tobias Philipp (12/27/2012 08:10 AM EDT)
***Marco Quargentan (12/27/2012 09:01 AM EDT)
Frank Methling (12/27/2012 09:37 AM EDT)
***Ioan Marius Popdan (12/27/2012 11:29 AM EDT)
Adriana Clerici (12/27/2012 01:54 PM EDT)
**Gundars Kokts (12/28/2012 03:53 AM EDT)
Vivek Ranjan Nema (12/28/2012 05:41 AM EDT)
***Albert Stadler (12/28/2012 06:56 PM EDT)
*Franciraldo Cavalcante Jr (12/29/2012 03:10 AM EDT)
Yuchen Wang (12/29/2012 07:18 AM EDT)
*Aditi Agrawal (12/29/2012 04:00 PM EDT)
***Aditya Pal (12/29/2012 06:32 PM EDT)
Sandeep Navada (12/29/2012 08:40 PM EDT)
***Pedro Fonseca (12/29/2012 10:56 PM EDT)
Seung Min "Brian" Park (12/29/2012 11:43 PM EDT)
Minxi Jiang (12/31/2012 04:41 AM EDT)
Shouky Dan & Tamir Ganor (12/31/2012 06:47 AM EDT)
**Don Gosiewski (12/31/2012 07:03 AM EDT)
*Sergey Grishaev (12/31/2012 12:37 PM EDT)
*Daniel Lincke (12/31/2012 05:42 PM EDT)
***Renato Fonseca (12/31/2012 07:13 PM EDT)
Jeff Steele (12/31/2012 10:05 PM EDT)
**Mutaamba Maasha (12/31/2012 11:18 PM EDT)
Bradley Sherman (01/01/2013 03:50 AM EDT)
*Amir Leshem (01/01/2013 07:19 AM EDT)
Jeffrey Boerner (01/01/2013 02:51 PM EDT)
***Manix Rock (01/01/2013 03:35 PM EDT)
**Danny Lynch (01/02/2013 06:41 AM EDT)
**Doug Wines (01/02/2013 03:34 PM EDT)


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