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: 01/08/2018 @ 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)
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)