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Define winning strategy (Posted on 2013-11-14) Difficulty: 3 of 5
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 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.

No Solution Yet Submitted by Ady TZIDON    
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Solution How to win. | Comment 1 of 6
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.

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

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