# Ponder This

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## January 2019 - Challenge

<< December

Alice and Bob are playing the following game: they start from a number N and each one of them in his or her turn (Alice starts) divides N by any divisor that is either a prime or a product of several distinct prime numbers. The winner is the one who gets to one - thus leaving the other player with no legal move.
To define the initial N, Alice chooses a number a from a set A, and a number b from a set B. The game is played with N=a+b. Charlie knows that Alice will start, and he wants to let Bob win. He does that by fixing the sets A and B.

He can do that, for example, by choosing A=[3,99] and B=[1,22]. (Why?)

Your challenge, this month, is to help Charlie find sets A and B with at least four different numbers each, that will allow Bob to win.

Bonus '*' for solutions with more than 4 elements in the set B.

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: 30/12/2018 @ 12:00 PM EST
Solution: 02/02/2019 @ 12:00 PM EST
List Updated: 16/01/2019 @ 12:00 PM EST

*David Greer (31/12/18 02:06 AM IDT)
Andreas Stiller (31/12/18 02:15 AM IDT)
*Alper Halbutogullari (31/12/18 02:26 AM IDT)
Alexander Daryin (31/12/18 05:19 AM IDT)
Justin Rogers (31/12/18 07:59 AM IDT)
*Anders Kaseorg (31/12/18 08:45 AM IDT)
Bert Dobbelaere (31/12/18 01:20 PM IDT)
Thomas Huet (31/12/18 02:18 PM IDT)
*Florian Fischer (31/12/18 04:43 PM IDT)
Eden Saig (31/12/18 06:12 PM IDT)
JJ Rabeyrin (31/12/18 06:28 PM IDT)
*Deron Stewart (01/01/19 12:31 AM IDT)
*Haye Chan (02/01/19 08:53 AM IDT)
Graham Hemsley (02/01/19 10:42 AM IDT)
Hugo Pfoertner (02/01/19 12:52 PM IDT)
*Adam Daire (02/01/19 21:13 PM IDT)
Noam Lasry (03/01/19 01:00 AM IDT)
Reiner Martin (03/01/19 01:52 AM IDT)
Rashid Naimi (03/01/19 05:49 AM IDT)
Adrienne Stanley (04/01/19 12:56 AM IDT)
*Paolo Farinelli (04/01/19 02:02 AM IDT)
*Emma Kee (04/01/19 11:47 AM IDT)
*Jess Thrysoee (04/01/19 01:16 AM IDT)
*Dieter Beckerle (05/01/19 10:44 AM IDT)
*Harald Bögeholz (05/01/19 02:48 PM IDT)
*Antonio García Astudillo (06/01/19 01:52 AM IDT)
*Walter Schmidt (06/01/19 09:29 AM IDT)
*David F.H. Dunkley (06/01/19 12:00 PM IDT)
*Daniel Bitin (06/01/19 07:31 PM IDT)
Daniel Chong Jyh Tar (07/01/19 10:19 AM IDT)
Charles Joscelyne (08/01/19 01:51 AM IDT)
Victor Chang (08/01/19 08:30 AM IDT)
**Uoti Urpala (08/01/19 08:34 AM IDT)
*Vladimir Volevich (08/01/19 08:52 AM IDT)
Louis Faucon (08/01/19 10:21 AM IDT)
*David Stevens (08/01/19 11:45 AM IDT)
*Todd Will (09/01/19 08:17 PM IDT)
*Loukas Sidiropoulos (09/01/19 04:07 PM IDT)
*Kang Jin Cho (11/01/19 08:23 AM IDT)
*Haye Chan (11/01/19 10:32 AM IDT)
*Dieter Dobbelaere (11/01/19 04:16 PM IDT)
Armin Krauss (11/01/19 09:29 PM IDT)
Kelvin Kim (12/01/19 06:04 PM IDT)
Young Joon Kim (12/01/19 06:21 PM IDT)
Jeewoo Lee (12/01/19 07:30 PM IDT)
Joonsoo Lee (12/01/19 08:16 PM IDT)
Almog Yair (13/01/19 01:13 PM IDT)
*Dominik Reichl (13/01/19 02:06 PM IDT)
Joehyun Kim (13/01/19 03:12 PM IDT)
Jiho Lee (13/01/19 08:08 PM IDT)
Cynthia Beauchemin (13/01/19 09:37 PM IDT)
Rajko Nenadov (13/01/19 10:00 PM IDT)
Rustam Salikhov (14/01/19 09:36 AM IDT)