Yes you have a constant number of states at your disposal. Otherwise, there is a trivial solution that takes n or so time, matching the theoretical lower bound (imposed by the "speed of light" for information propagation in this kind of automaton), rendering the problem thoroughly uninteresting.

>Assuming that there is a fixed number of states, regardless of how many soldiers there are in the line...

I think that this line may be your best indication. How exactly should you interpret this sentence? I don't know!