They both started playing a game called " donate the money " !

The rule of this game is that only one can win and he can't have more money than the other.

Given that situation , we can easily see that Alan will win because of his 3 $, as 3 < 4 , put simply, he who has higher money, will donate the other first n $ at a time(where n = 1,2,3,....keep increasing each turn), when the donation is finished, who has less money will be the winner.

Say, Mike gives 1 $ to Alan, Alan will have now 4 $, then Alan will give Mike 2 $(second turn), so Mike will now have 5 $ .. thus continues..

Given these things can you determine who will always win if you are given the money amount?

If so, let's see who will win if both has 55 $ each and the turn could be anyone's :D

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