# Ponder This

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## January 2019 - Challenge

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: 02/02/2019 @ 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)
*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)
Mykola Zubach (16/01/19 11:25 AM IDT)
*Shouky Dan & Tamir Ganor (17/01/19 08:49 AM IDT)
Alex Fleischer (17/01/19 08:58 AM IDT)
Joseph DeVincentis (17/01/19 06:23 PM IDT)
Francis Golding (18/01/19 03:01 PM IDT)
Danny Antonetti (19/01/19 05:05 AM IDT)
Marco Bellocchi (20/01/19 12:50 AM IDT)
Taeyang David Park (20/01/19 06:54 PM IDT)
*Boris Silantyev (21/01/19 11:52 AM IDT)
Yi Won Kim (22/01/19 04:22 AM IDT)
Denys Kopiychenko (22/01/19 05:56 AM IDT)
Phil Muhm (22/01/19 09:45 PM IDT)
*Atul Gupta (23/01/19 01:49 AM IDT)
Tyler Mullen (23/01/19 03:00 AM IDT)
Michael Rosola (23/01/19 06:36 PM IDT)
**Tom Sirgedas (24/01/19 12:24 AM IDT)
Eric Edward Pauley (24/01/19 10:02 AM IDT)
*Pieter Vandercammen (25/01/19 12:28 AM IDT)
DukeBG (25/01/19 02:45 PM IDT)
Klaus Hoffmann (25/01/19 07:44 PM IDT)
Deane Stewart (25/01/19 09:20 PM IDT)
Motty Porat (27/01/19 12:32 AM IDT)
Andrew Lee (27/01/19 03:33 PM IDT)
Andreas Knüpfer (27/01/19 06:22 PM IDT)
*Toke Eskildsen (27/01/19 08:40 PM IDT)
Henry Lee (27/01/19 08:51 PM IDT)
Jingran Lin (28/01/19 02:19 AM IDT)
Fabio Filatrella (28/01/19 02:30 PM IDT)
Luke Pebody (29/01/19 04:32 AM IDT)
*Chris Shannon (29/01/19 04:36 AM IDT)
Dan Dima (29/01/19 03:21 PM IDT)
*Aviv Nisgav (30/01/19 09:35 AM IDT)
Robert Lang (31/01/19 06:56 PM IDT)
Erik Wünstel (31/01/19 06:57 PM IDT)
Radu-Alexandru Todor (01/02/19 02:20 AM IDT)
**Oscar Volpatti (01/02/19 05:36 AM IDT)
Noam Zaks & Ayal Zaks (02/02/19 06:54 PM IDT)