Suppose three gunmen are A, B, and C who have a probability of 100%, 50% and 33% respectively. The shooting will start from C, then B and at last A. Now there are several possibilities for C. If C shoots B, then A would shoot C with an accuracy of 100% or in other case if C shoots A, then B would shoot him with an accuracy of 50%. So he has a probability of getting killed. We can see in either of the cases C will die. So what C will do in first round is that it will fire the shot in air. Now the scenario gets interesting. By doing this C has turned the battle among three people into two people A and B. This will increase the chances of survival of C. So now its B's turn of firing. So he can fire at either A or C. If B fires at C, then A will shoot B with an accuracy of 100% and B knows that he will surely die so B won't do that. If B shoots A, then C will shoot B. I think this is the solution. Please point out if there are any loopholes.
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