Wilson was slightly vague stating the problem, I assume he meant uniform random speeds in [0,1] for the bullet, one bullet shot each clock tick. Computer simulations would be a good idea. Draw trajectories (each a straight line segment) in the space-time plane. As soon as two lines hit they vanish. So no two can cross. Each line has 0<slope<1. Each line has one vertex on the time-axis at integer locations, rest lies in the right halfplane (can ignore left halfplane). There is a hierarchical structure: the planar dual of the diagram is a tree. It seems likely to me there is some sort of statistical self-similarity property, the statistics at level L above leaves of the tree should be the same everywhere (if L held fixed) and depend on L like a power, exponential, or logarithmic law. So I would predict the typical distance attained before vanish for a level-L bullet depends on L like that. If this kind of thing can be understood then the problem should be solved (including nonrigorous understanding leading to nonrigorous solution). -- Warren D. Smith http://RangeVoting.org