August 2018 - Challenge

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There is a well-known riddle about two friends (Alice and Bob) who went walking in the desert.
Alice had two gallons of water and Bob had three gallons.
They met Charlie who had no water at all and they all (Alice, Bob, and Charlie) shared the five gallons of water evenly.
As a token of his gratitude, Charlie gave them five gold coins.
What is the fair way to split these five coins?
Hint: it is *not* the obvious two to Alice and three to Bob. (Why?)

Our challenge this month is to solve a similar problem:
In J.R.R. Tolkien's works, nine rings were given to humans. Our challenge is this: Each one of the nine ring holders brought W_i droplets of water (W_1, W_2, W_3, ..., W_9).
Sauron (who had the one ring to rule them all) came without any water at all. They all shared their water; and each one of the ring holders got G_i (G_1, G_2, G_3, ..., G_9) tiny nuggets of gold in return. Where W_1+W_2+...+W_9 = G_1+G_2+...+G_9.
However, the 18 W_i and G_i water droplet and gold nugget amounts, respectively, are all different and at least 17 of them are prime numbers.
Find the nine W_i's.




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: 30/07/2018 @ 12:00 PM EST
Solution: 02/09/2018 @ 12:00 PM EST
List Updated: 03/09/2018 @ 12:00 PM EST

People who answered correctly:

Daniel Chong Jyh Tar (30/07/18 02:03 PM IDT)
Andreas Eisele (30/07/18 03:29 PM IDT)
Noam Lasry (30/07/18 04:45 PM IDT)
Bert Dobbelaere (30/07/18 08:03 PM IDT)
Sean Egan (30/07/18 08:19 PM IDT)
Hao Zheng (30/07/18 10:28 PM IDT)
JJ Rabeyrin (31/07/18 12:36 AM IDT)
Harald Bögeholz (31/07/18 06:00 AM IDT)
Dong Lingyun, Alistair Ong & Ma Hongqiang (31/07/18 09:27 AM IDT)
Steven Langerwerf (31/07/18 10:18 AM IDT)
Alex Fleischer (31/07/18 10:55 AM IDT)
Reiner Martin (31/07/18 11:31 AM IDT)
Alper Halbutogullari (31/07/18 11:36 AM IDT)
Paul Shaw (31/07/18 12:30 PM IDT)
Thomas Egense (31/07/18 02:00 PM IDT)
Guillaume Escamocher (31/07/18 02:05 PM IDT)
Thomas Egense (31/07/18 02:17 PM IDT)
Stijn Theunis (31/07/18 05:25 PM IDT)
Jordan Rinder (31/07/18 05:29 PM IDT)
Stijn Theunis (31/07/18 05:25 PM IDT)
Jordan Rinder (31/07/18 05:29 PM IDT)
Eden Saig (01/08/18 01:03 AM IDT)
Rickard Björklund (01/08/18 02:12 AM IDT)
Almog Yair (01/08/18 02:59 AM IDT)
Susanne Wienand (01/08/18 10:48 AM IDT)
Harold Gutch (01/08/18 12:34 PM IDT)
Alex Ang (01/08/18 04:26 PM IDT)
Keith Schneider (01/08/18 07:29 PM IDT)
Joseph Berman (01/08/18 08:25 PM IDT)
Nicolas Ayotte (01/08/18 08:57 PM IDT)
Sean Egan (01/08/18 09:49 PM IDT)
Loukas Sidiropoulos (02/08/18 12:37 AM IDT)
Vladimir Volevich (02/08/18 05:19 AM IDT)
Allen Zhu (02/08/18 05:56 AM IDT)
Amos Guler (02/08/18 10:08 AM IDT)
Graham Hemsley (02/08/18 11:01 AM IDT)
Dieter Beckerle (02/08/18 11:12 AM IDT)
David Greer (02/08/18 01:20 AM IDT)
Ali Can Keserel (02/08/18 05:17 PM IDT)
Anna Judith (02/08/18 079:07 PM IDT)
Pi-Ching Liu (03/08/18 12:43 AM IDT)
Shirish Chinchalkar (03/08/18 03:08 AM IDT)
Vladimir Volevich (03/08/18 11:56 AM IDT)
Ian Sleightholme (03/08/18 03:31 PM IDT)
Prashant Wankhede (03/08/18 03:10 AM IDT)
Kang Jin Cho (03/08/18 08:56 PM IDT)
Francis Golding (03/08/18 06:43 PM IDT)
Andreas Stiller (03/08/18 11:24 PM IDT)
Sri Mallikarjun J (03/08/18 11:56 PM IDT)
Motty Porat (04/08/18 01:30 AM IDT)
Ricardo Koller (04/08/18 03:03 AM IDT)
Andreas Knüpfer (04/08/18 11:34 AM IDT)
Thomas Huet (04/08/18 03:48 PM IDT)
Raymond Lo (04/08/18 03:58 PM IDT)
Joaquim Neves Carrapa (04/08/18 04:00 PM IDT)
Parth Trivedi (04/08/18 04:38 PM IDT)
Armin Krauß (04/08/18 04:54 PM IDT)
Michael Liepelt (04/08/18 10:10 PM IDT)
Todd Will (04/08/18 11:02 PM IDT)
Kipp Johnson (04/08/18 11:54 PM IDT)
Emir Haleva (05/08/18 12:33 AM IDT)
David F.H. Dunkley (05/08/18 10:30 AM IDT)
Tyler Mullen (05/08/18 12:00 PM IDT)
Mathias Schenker (05/08/18 01:35 PM IDT)
Daniel Bitin (05/08/18 02:52 PM IDT)
Ritesh Ranjan (05/08/18 05:44 PM IDT)
Florian Fischer (05/08/18 06:42 PM IDT)
Shouky Dan & Tamir Ganor (05/08/18 09:39 PM IDT)
Fabio Michele Negroni (05/08/18 10:21 PM IDT)
Zhang Dingwen (06/08/18 11:27 AM IDT)
Rustam Salikhov (06/08/18 02:54 PM IDT)
Brian Pietsch (06/08/18 03:47 PM IDT)
Joseph DeVincentis (06/08/18 03:52 PM IDT)
Marcel Caria (06/08/18 05:01 PM IDT)
Adrian Neacsu (06/08/18 05:57 PM IDT)
Lavanya Kannan (06/08/18 06:06 PM IDT)
Gale Greenlee (07/08/18 12:44 AM IDT)
Soumitra Agarwal (07/08/18 08:54 AM IDT)
Clive Tong (07/08/18 01:03 PM IDT)
Luke Pebody (08/08/18 03:30 PM IDT)
Rachit Srivastava (08/08/18 08:17 PM IDT)
Andrejs Pilka (09/08/18 09:00 AM IDT)
Arthur Vause (09/08/18 04:02 PM IDT)
Davin Choo (11/08/18 09:50 AM IDT)
Amaury Garrec (11/08/18 01:24 PM IDT)
Hugo Pfoertner (11/08/18 09:37 PM IDT)
Kurt Foster (11/08/18 09:42 PM IDT)
Lakshman inkulu (12/08/18 03:19 PM IDT)
Kurt Foster (12/08/18 04:22 PM IDT)
Danny Antonetti (12/08/18 08:15 PM IDT)
Robert Lang (13/08/18 09:59 AM IDT)
Chuck Carroll (13/08/18 01:38 PM IDT)
Ehud Aharoni & Omri Soceanu(14/08/18 05:00 PM IDT)
Siddhartha Srivastava (14/08/18 05:17 PM IDT)
Boris Rakus (15/08/18 04:49 PM IDT)
Charles Joscelyne (15/08/18 06:39 PM IDT)
Dominik Reichl (15/08/18 08:25 PM IDT)
Tilo Anschütz (16/08/18 11:43 AM IDT)
Yuxuan Shui (17/08/18 07:56 PM IDT)
Li Li (18/08/18 08:16 PM IDT)
Franciraldo Cavalcante (19/08/18 06:38 PM IDT)
Hanlin Ren (20/08/18 04:09 PM IDT)
Alexander Raß (20/08/18 04:25 PM IDT)
Feyzullah Egriboyun (21/08/18 01:23 AM IDT)
Mehmet Saruhan (21/08/18 09:21 AM IDT)
Stephane Vaillant (21/08/18 04:49 PM IDT) Heidi Stockton (23/08/18 06:56 PM IDT)
Oscar Volpatti (24/08/18 07:03 PM IDT)
Sergey Koposov (25/08/18 02:14 AM IDT)
Sergey Subbotin (25/08/18 04:53 PM IDT)
Lorenz Reichel (25/08/18 11:26 PM IDT)
Nathaniel Litton (27/08/18 12:51 AM IDT)
Mykola Zubach (27/08/18 09:04 AM IDT)
Xiao Liu (28/08/18 05:30 AM IDT)
Jimmy Waters (28/08/18 06:30 PM IDT)
Atul Gupta (28/08/18 09:36 PM IDT)
Daniel Son (30/08/18 08:17 PM IDT)
Paolo Farinelli (30/08/18 10:05 PM IDT)
Oleg Vlasii (31/08/18 10:06 AM IDT)
Muralidhar Seshadri (31/08/18 11:21 PM IDT)
Radu-Alexandru Todor (01/09/18 01:53 AM IDT)
itsik horovitz (01/09/18 10:55 PM IDT)
Radu-Alexandru Todor (02/09/18 08:36 PM IDT)