IBM Ponder This #249 · January 2019

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.

Solution

Best opened after a real attempt

To be added.