Start with the set S of the first 25 natural numbers: S={1,2,…,25}.

Player A first picks an even number x

_{0}and removes it from S:

We have S:=S−x

_{0}.

Then they take turns (starting with B) picking a number x

_{n}∈S which is either divisible by x

_{n-1}or divides x

_{n-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.