Two players A and B play the following game:
Start with the set S of the first 25 natural numbers: S={1,2,…,25}.
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 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.

There are four numbers which can only be followed by a choice of 1:  13, 17, 19, 23.

Player A can win by starting with any of these. 
Player B will be forced to choose 1.
Player A can respond by choosing another of these.
Player B loses because 1 is no longer available.

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Edit: 
This does not follow the rule that A must start by picking an even number. 
So it is a simple solution to an easier problem.

Edited on November 18, 2013, 9:05 am

Posted by Jer on 2013-11-15 09:08:43