Hi funsters, A colleague posed the following question: --------- You are shooting at a submarine that is moving through Z/nZ at constant velocity -- that is, its position at time t is a+bt (mod n), for some 0 <= a,b < n -- but you don't know a or b. At each time t=0,1,2,..., you can shoot at one position. How quickly can you hit all possible submarines? --------- Well, he actually asked about n = one million, but you get the idea. I hadn't seen this before; anyone recognize it? I have a plausibly efficient answer, but no proof that it's optimal. I'll wait a few days before sending my heuristic, to give y'all a chance to think about it without contamination. --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.