IBM Research | Ponder This | December 2012 challenges

# Ponder This

## December 2012

<<November December January>>

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

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)
***Øyvind 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)
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)
**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)

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