Interesting answers, but not for the right reason.

The key here for game theory is that you have to make a few reasonable assumptions.

Charlie should simply shoot straight up into the air, but most importantly not at either Adam or Brian.

The logic here is simple - If Charlie hits either Brian or Adam, then it will become the surviving persons shot next, with only one target - Charlie!

However, if Charlie hits neither, it is reasonable to assume that Brian will make the same assumption that everyone else has, and would do - that it is better to risk being shot at by Charlie, than by Adam. So Brian will logically shoot Adam.

This means that it is now Charlies shot again! This only leaves Charlie to shoot Brian (if he doesnt miss!!!)

The issue here is that assuming that all will hit their target (as is often the way in a duel given the distances involved), whoever shoots someone else first pretty much guarantees his own death.

Cool, eh!

JJ