Ponder This Challenge - September 2015 - Awarding N people with 8 multi-person teams

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).

Solution

• Click here to view the solution

  The best solution, for the first 4 cases, is the Fibonacci sequence (2; 2,3; 2,3,5; 2,3,5,8).

  For 8 teams, we can do better by choosing powers of 2 +1 and fixing the end: 2,3,5,9,17,33,65,70; but there is an even better solution: 2,3,5,8,16,24,54,78. This is the optimal one.

Solvers

• 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)
• 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)