Say with Michael K. that v[n] denotes the velocity of the farthest bullet right after time n. The simplest discretization of the problem, a la Jim, may be this version: Instead of the velocities being chosen from the uniform distribution on [0,1], let them be chosen from the set {1,2,3,...,K} with each having probability 1/K. This may shed light on the original problem. ----- If the answer to the original question is Yes, (*) v[n] -> 1 as n -> oo (with probability 1), then it may be easier to first show that (**) lim sup {v[1],v[2],v[3],...,v[n],...} = 1 (with probability 1). Or, maybe (**) is true and (*) isn't. ((( If I had to guess, I'd say that (*) is probably not true, because the fastest bullets are not necessarily the ones that go farthest, but are often the ones that annihilate soonest. ))) --Dan David wrote: << A gun sits on a line. Every second, the gun shoots a bullet to the right at a random constant speed between 0 and 1. If two bullets collide they annihilate. It's probability 0, but if more than two bullets collide, the slowest bullets annihilate in pairs. Can we expect the speed of the furthest bullet to approach 1 over time?
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