Dima live dormitory cockroachesAt moment 0 Dima see cockroach running table decide kill Dima need exactly t second aim precisely strike cockroach finish itTo survive cockroach run shadow cast round plate stand table T second Shadow casted plate shape circle Shadow circle intersect nest overlap arbitrarilythe cockroach use follow strategy equiprobably pick direction run run constant speed v if moment tt reach shadow circle immediately stop shadow stay alive Otherwise cockroach kill Dimas precise strike consider Dimas precise strike instantdetermine probability cockroach stay alive