Two players A and B play the following game:
Start with the set S of the first 25 natural numbers:
Player A first picks an even number x0 and removes it from S:
We have S:=S−x0.
Then they take turns (starting with B) picking a number xn∈S which is either divisible
by xn-1 or divides xn-1 and removing it from S.
The player who can not find a number in S which is a multiple of the previous number or is divisible by it loses.
Which player has the winning strategy and what is it?
Source: someone sent it by Email.