IBM Research | Ponder This | January 2016 challenges

# Ponder This

## January 2016

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Ponder This Challenge:

As part of IBM's efforts to make a better and greener planet, this month's challenge is to design an efficient gear system for bicycles. The front chainrings (S_1) and back cogset (S_2) are represented by two sets of numbers S_1 and S_2 where each gear g is the product of two numbers, one from each set: s_1*s_2. When designing the gears, we need sets of numbers that can produce every gear value between 1 and N up to +/- 1, i.e., for every number m between 1 and N there exists s_1 in S_1 and s_2 in S_2 such that abs(m-s_1*s_2)<=1.

So, for example, using sets of size 3, we can get to N=19 by S_1={1,3,6} and S_2={2,3,5}.

Your challenge is to find the values of S_1 and S_2 of size 6 that solve the problem for N=56 (again, using +/- 1); Earn an asterisk for a significant increase of N.

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: 28/12/2015 @ 12:00 PM EST
Solution: 01/02/2016 @ 12:00 PM EST
List Updated: 04/02/2016 @ 12:00 PM EST

*Robert Gerbicz (29/12/2015 03:10 PM IDT)
Lorenz Reichel (29/12/2015 03:36 PM IDT)
Kang Jin Cho (29/12/2015 07:00 PM IDT)
Daniel Johnson-Chyzhykov (29/12/2015 08:25 PM IDT)
Dieter Beckerle (29/12/2015 09:48 PM IDT)
*Radu-Alexandru Todor (30/12/2015 01:58 AM IDT)
Sean Egan (30/12/2015 11:17 AM IDT)
James Dow Allen (30/12/2015 11:59 AM IDT)
Bruce Norskog (30/12/2015 08:25 PM IDT)
Wayne Petrychyn (30/12/2015 10:18 PM IDT)
Jesse Rearick (30/12/2015 10:18 PM IDT)
Janos Csorba (31/12/2015 01:24 AM IDT)
Jean-Baptiste Rouquier (31/12/2015 10:45 AM IDT)
Shouky Dan & Tamir Ganor (31/12/2015 11:13 AM IDT)
Dejan Stakić (31/12/2015 12:28 PM IDT)
*Yan-Wu He (31/12/2015 02:17 PM IDT)
Alex Fleischer (31/12/2015 03:05 PM IDT)
Alexandre Ferrand (31/12/2015 03:39 PM IDT)
Boris Kazimir Hostnik (31/12/2015 04:25 PM IDT)
Gary M. Gerken (31/12/2015 06:45 PM IDT)
*Rob Pratt (31/12/2015 09:19 PM IDT)
Harald Bögeholz (31/12/2015 11:32 PM IDT)
Matt Falk (01/01/2016 04:50 AM IDT)
Brendan Berger (01/01/2016 07:13 AM IDT)
Adrian Neacsu (01/01/2016 12:50 PM IDT)
Gregory Giecold (01/01/2016 06:09 PM IDT)
Michael Gottlieb (01/01/2016 08:38 PM IDT)
Ji Eun Kim (01/01/2016 09:25 PM IDT)
Todd Will (01/01/2016 10:10 PM IDT)
Mathias Schenker (01/01/2016 10:28 PM IDT)
Seung Hwan (Sonny) An (02/01/2016 12:24 AM IDT)
Shirish Chinchalkar (02/01/2016 02:00 AM IDT)
Philip Adams (02/01/2016 03:40 AM IDT)
Rahul Upakare (02/01/2016 10:16 AM IDT)
Steven Langerwerf (03/01/2016 12:46 AM IDT)
Sergey Koposov (03/01/2016 12:14 PM IDT)
Amos Guler (03/01/2016 12:23 PM IDT)
*Andreas Stiller (03/01/2016 09:23 PM IDT)
Boris Rakus (03/01/2016 10:06 PM IDT)
Jesus Sanz (03/01/2016 10:28 PM IDT)
Igor Karp (03/01/2016 11:58 PM IDT)
Liubing Yu (04/01/2016 01:56 AM IDT)
*Phil Benamy (04/01/2016 03:18 AM IDT)
Joseph DeVincentis (04/01/2016 04:29 AM IDT)
Ajay Mallepally (04/01/2016 05:52 AM IDT)
Shaleen Deep (04/01/2016 09:47 AM IDT)
Alex Teich (04/01/2016 02:38 PM IDT)
Timothy S. Lewis (04/01/2016 05:20 PM IDT)
Ali Can Keserel (04/01/2016 06:13 PM IDT)
Curtis Watson (04/01/2016 07:11 PM IDT)
Rogerio Ponce da Silva (04/01/2016 10:35 PM IDT)
Michael Liepelt (04/01/2016 11:19 PM IDT)
Tom Sirgedas (05/01/2016 01:43 AM IDT)
Victor Chang (05/01/2016 09:02 AM IDT)
Umut Uludag (05/01/2016 09:42 AM IDT)
Lorenzo Gianferrari Pini (05/01/2016 09:59 AM IDT)
Reiner Martin (05/01/2016 10:11 AM IDT)
Raymond Lo (05/01/2016 01:23 PM IDT)
Pål Hermunn Johansen (05/01/2016 01:54 PM IDT)
*Donald T Dodson (05/01/2016 05:05 PM IDT)
Clive Tong (05/01/2016 11:04 PM IDT)
Rajesh Sathiyanarayanan (06/01/2016 10:22 AM IDT)
Hendrik Nigul (06/01/2016 01:10 PM IDT)
Mark J Murphy (06/01/2016 10:06 PM IDT)
Erdinc Ozturk (06/01/2016 11:56 PM IDT)
Minxi Jiang (07/01/2016 02:34 AM IDT)
Ajit Thyagarajan (07/01/2016 07:01 AM IDT)
Francis Golding (07/01/2016 12:04 PM IDT)
Roberto Tauraso (07/01/2016 12:46 PM IDT)
Tero Patana (07/01/2016 11:17 PM IDT)
Jan Rothkegel (08/01/2016 09:47 AM IDT)
Cody Pfau (08/01/2016 11:42 PM IDT)
Yuval Salant (09/01/2016 12:01 AM IDT)
Levent Ertoz (09/01/2016 01:49 AM IDT)
Jimmy Waters (09/01/2016 04:58 AM IDT)
Claudio Hüni (09/01/2016 08:41 PM IDT)
Di Luo (10/01/2016 05:12 AM IDT)
Aviv Nisgav (10/01/2016 11:06 AM IDT)
*Paolo Farinelli (10/01/2016 11:07 AM IDT)
Daniel Bitin (10/01/2016 05:07 PM IDT)
Kwonil Kobe Ko (10/01/2016 08:26 PM IDT)
Fabio Michele Negroni (10/01/2016 09:43 PM IDT)
Peter Gerritson (10/01/2016 11:32 PM IDT)
Kipp Johnson (11/01/2016 12:41 AM IDT)
Christian Pfaffenzeller (11/01/2016 12:40 PM IDT)
Dan Salajan (11/01/2016 05:31 PM IDT)
Phillip Ahn (12/01/2016 04:17 AM IDT)
Viola Lee (12/01/2016 05:00 AM IDT)
Heidi Kim (12/01/2016 08:09 AM IDT)
Evert van Dijken (12/01/2016 04:56 PM IDT)
ByeongYeon (Jackie) Ryu (12/01/2016 05:33 PM IDT)
Yeonjune Kang (12/01/2016 11:54 PM IDT)
Hyun Jin Kim (13/01/2016 02:55 AM IDT)
Jason Lee (13/01/2016 10:55 AM IDT)
Emir Haleva (13/01/2016 05:14 PM IDT)
Myong Claire Yun (13/01/2016 05:36 PM IDT)
Emilio Del Tessandoro (13/01/2016 06:33 PM IDT)
Anton Čotar (14/01/2016 01:17 AM IDT)
Nadir S (14/01/2016 11:52 AM IDT)
Tomáš Jurík (14/01/2016 03:38 PM IDT)
Michael Blaszczyk (15/01/2016 07:19 PM IDT)
Albert Stadler (16/01/2016 10:45 PM IDT)
Ayaskant Pani (18/01/2016 03:37 AM IDT)
Benjamin Lui (18/01/2016 04:19 AM IDT)
Hamidreza Bidar (18/01/2016 09:00 PM IDT)
Fabio Filatrella (19/01/2016 03:42 PM IDT)
Franciraldo Cavalcante (20/01/2016 06:44 AM IDT)
Thomas Egense (20/01/2016 10:04 AM IDT)
Tilo Anschütz (20/01/2016 03:11 PM IDT)
Simon Foster (21/01/2016 10:52 AM IDT)
Guillem Collell Talleda (21/01/2016 11:44 AM IDT)
Zachary Powers (21/01/2016 07:53 PM IDT)
Anders Bisbjerg Madsen (21/01/2016 10:17 PM IDT)
Ioan Marius Popdan (22/01/2016 02:45 PM IDT)
Abhishek Gupta (23/01/2016 12:24 AM IDT)
Lawrence Hon (23/01/2016 05:10 PM IDT)
Junjiajia Long (24/01/2016 06:17 PM IDT)
Hyun Min Victoria Woo (24/01/2016 06:37 PM IDT)
Alex Zdan (24/01/2016 08:48 PM IDT)
Guenter Nowak (25/01/2016 03:44 AM IDT)
David Dunkley (25/01/2016 09:16 AM IDT)
Amit Bhatia (25/01/2016 10:05 PM IDT)
Tim Cieplowski (26/01/2016 01:21 AM IDT)
*Chris Shannon (26/01/2016 09:01 AM IDT)
Andreas Wohlfrom (26/01/2016 11:14 AM IDT)
Mihail Plesa (26/01/2016 08:31 PM IDT)
Gyorgy Gyomai (26/01/2016 08:45 PM IDT)
Loukas Sidiropoulos (26/01/2016 09:34 PM IDT)
Rudy Cortembert (26/01/2016 10:05 PM IDT)
Stéphane Higueret (27/01/2016 12:33 PM IDT)
Jitesh Jain (28/01/2016 01:47 AM IDT)
*Nyles Heise (28/01/2016 04:51 AM IDT)
Armin Krauss (28/01/2016 03:31 PM IDT)
Motty Porat (29/01/2016 02:24 AM IDT)
Nicolas Bitouze (29/01/2016 04:42 AM IDT)
Mike Chirozzi (29/01/2016 05:44 AM IDT)
Toke Eskildsen (30/01/2016 11:04 AM IDT)
Martin Sergio H. Faester (31/01/2016 04:44 PM IDT)
Cindy Sewon Park (31/01/2016 07:10 PM IDT)
Ryunhyung Jessica Kim (31/01/2016 07:35 PM IDT)
Colas Kerkhove (31/01/2016 07:53 PM IDT)
Erik Wünstel (31/01/2016 11:33 PM IDT)
David Greer (31/01/2016 11:30 PM IDT)
Yun Jin Jeong (01/02/2016 03:31 AM IDT)
Muralidhar Seshadri (01/02/2016 05:34 AM IDT)
Oscar Volpatti (01/02/2016 08:07 AM IDT)