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.
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30/12/2018 @ 12:00 PM EST Solution:
02/02/2019 @ 12:00 PM EST List Updated:
16/01/2019 @ 12:00 PM EST
People who answered correctly:
*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)