IBM Research | Ponder This | September 2015 challenges

# Ponder This

## September 2015

<<August September October>>

Ponder This Challenge:

IBM decided to give an award for technical excellence to exactly N people.
Several teams submitted their nominations.
Many of them are single-person teams, but 8 are multi-person teams of more than 1 member.
It so happens that the size of the teams is such that awards can be given to any number of teams, from 1 to N, while keeping the total number of people exactly N.
Find the sizes of the 8 teams that enable the maximal N.

There is a better solution (N > 6) for 4 teams, but a possible answer to the same question with 4 multi-person teams and N=6 is: 2,3,3,6; since you can award a single team (6); 2 teams (3,3); 3 teams (1,2,3); 4 teams (1,1,1,3); 5 teams (1,1,1,1,2); and 6 teams (1,1,1,1,1,1).

Update (3/9):

1. You can do better than 56.

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: 27/08/2015 @ 12:00 PM EST
Solution: 01/10/2015 @ 12:00 PM EST
List Updated: 06/10/2015 @ 12:00 PM EST

Robert Gerbicz (31/08/2015 05:19 PM IDT)
Daniel Bitin (31/08/2015 06:23 PM IDT)
Don Dodson (31/08/2015 06:50 PM IDT)
Joseph DeVincentis (31/08/2015 07:42 PM IDT)
James Dow Allen (31/08/2015 07:56 PM IDT)
Lorenz Reichel (01/09/2015 01:12 AM IDT)
Yan-Wu He (01/09/2015 03:38 AM IDT)
David Greer (01/09/2015 06:40 AM IDT)
Jesse Rearick (01/09/2015 06:40 AM IDT)
Todd Will (01/09/2015 03:50 PM IDT)
Peter Mora (02/09/2015 10:33 AM IDT)
Janos Csorba (02/09/2015 11:56 AM IDT)
Hamidreza Bidar (02/09/2015 01:01 PM IDT)
Uoti Urpala (03/09/2015 06:39 PM IDT)
Donald Dodson (03/09/2015 07:04 PM IDT)
Joe Kelley (03/09/2015 08:26 PM IDT)
Xin Lu (03/09/2015 09:35 PM IDT)
Andreas Stiller (03/09/2015 09:40 PM IDT)
Dieter Beckerle (04/09/2015 02:06 PM IDT)
Michael Slifker (05/09/2015 12:56 AM IDT)
Mathias Schenker (05/09/2015 11:25 AM IDT)
Sean Egan (05/09/2015 11:53 AM IDT)
Peter Gerritson (05/09/2015 04:59 PM IDT)
Shirish Chinchalkar (05/09/2015 11:58 PM IDT)
Bart De Vylder (06/09/2015 12:45 AM IDT)
Amos Guler (06/09/2015 10:27 AM IDT)
Rajesh Sathiyanarayanan (06/09/2015 02:06 PM IDT)
Graham Hemsley (06/09/2015 04:37 PM IDT)
Gary M. Gerken (06/09/2015 08:19 PM IDT)
Kyle Askine (07/09/2015 07:06 AM IDT)
William Heller (07/09/2015 07:47 AM IDT)
Kang Jin Cho (07/09/2015 03:00 PM IDT)
LaurV (07/09/2015 06:05 PM IDT)
Arthur Vause (07/09/2015 11:26 PM IDT)
José Eduardo Gaboardi de Carvalho (08/09/2015 01:26 AM IDT)
Rob Pratt (08/09/2015 06:45 PM IDT)
Liubing Yu (08/09/2015 08:32 PM IDT)
Kevin Bauer (09/09/2015 08:52 AM IDT)
Hongcheng Zhu (09/09/2015 10:54 AM IDT)
Andreas Eisele (09/09/2015 11:17 AM IDT)
Eitan Levine (09/09/2015 11:32 AM IDT)
Seth Cohen (09/09/2015 05:45 PM IDT)
Reiner Martin (10/09/2015 09:02 AM IDT)
Motty Porat (10/09/2015 12:29 AM IDT)
Paolo Farinelli (10/09/2015 03:57 PM IDT)
Colman Humphrey (10/09/2015 06:38 PM IDT)
Ran Sharon (10/09/2015 07:38 PM IDT)
Sergey Koposov (11/09/2015 01:09 PM IDT)
Luke Hsieh (11/09/2015 10:34 PM IDT)
Assaf Bar-Yaacov (12/09/2015 03:57 AM IDT)
Emil Pedersen (12/09/2015 10:37 AM IDT)
George Stoianov (12/09/2015 02:05 PM IDT)
Ali Can Keserel (12/09/2015 07:35 PM IDT)
Muralidhar Seshadri (12/09/2015 08:41 PM IDT)
Hao Wu (13/09/2015 11:44 AM IDT)
Zheng Yan (13/09/2015 04:19 PM IDT)
Dan Dima (13/09/2015 06:10 PM IDT)
Colas Kerkhove (14/09/2015 11:32 AM IDT)
Francis Golding (14/09/2015 01:27 PM IDT)
Bryce Herdt (14/09/2015 10:55 PM IDT)
Radu-Alexandru Todor (15/09/2015 12:51 A IDT)
Ricardo Koller (16/09/2015 12:37 AM IDT)
Ingmar Dasseville (16/09/2015 04:40 PM IDT)
Randi Pedersen (17/09/2015 11:34 AM IDT)
Justin C. Archer (17/09/2015 03:13 PM IDT)
Armin Krauss (17/09/2015 04:33 PM IDT)
Dan Salajan (18/09/2015 02:59 PM IDT)
Benjamin Phillabaum (18/09/2015 04:15 PM IDT)
Di Luo (19/09/2015 07:41 AM IDT)
Adrien Ball (20/09/2015 08:54 PM IDT)
Hakan Summakoğlu (20/09/2015 11:43 PM IDT)
Tamir Ganor & Shouky Dan (21/09/2015 09:57 AM IDT)
Yochay Lustmann (21/09/2015 12:05 PM IDT)
Chris Shannon (22/09/2015 06:55 AM IDT)
David Dunkley (23/09/2015 01:32 AM IDT)
Huafeng Jiangv (23/09/2015 06:20 PM IDT)
Phil Benamy (24/09/2015 12:52 AM IDT)
Shawn Ligocki (24/09/2015 12:59 AM IDT)
Edwin Karat (24/09/2015 01:43 AM IDT)
Hakan Summakoğlu (24/09/2015 08:26 PM IDT)
Matthias Bussas (24/09/2015 11:21 PM IDT)
Zhang Chenzi (25/09/2015 03:42 PM IDT)
Dan Ismailescu (25/09/2015 04:17 PM IDT)
Kipp Johnson (25/09/2015 09:17 PM IDT)
Nyles Heise (26/09/2015 06:08 AM IDT)
Emilio Del Tessandoro (28/09/2015 12:05 AM IDT)
Frank Samm (28/09/2015 02:46 AM IDT)
Jitesh Jain (29/09/2015 02:09 AM IDT)
Björn Hendriks (29/09/2015 09:45 AM IDT)
Vladimir Dorofeev (29/09/2015 01:19 PM IDT)
Harald Bögeholz (29/09/2015 03:11 PM IDT)
Chaeyeon Oh (29/09/2015 06:17 PM IDT)
Leandro Araújo (29/09/2015 10:28 PM IDT)
Stéphane Higueret (29/09/2015 11:41 PM IDT)
Heidi Kim (30/09/2015 11:07 PM IDT)
Hyun Jin Kim (01/10/2015 12:31 AM IDT)
Ji Eun Kim (01/10/2015 12:43 AM IDT)
Balakrishnan Varadarajan (01/10/2015 05:45 AM IDT)
Bradley Sherman & Mason Bouffard (01/10/2015 09:09 AM IDT)
Kwonil Kobe Ko (01/10/2015 09:13 PM IDT)
Alexandre Gilotte (03/10/2015 04:56 PM IDT)