Statement

The OIS Enterprise is planning to open F new branches, each of them chosen from a pool of N possible cities. Each of the cities is located beside to the Sun Highway, at a distance of K_i, i=0,… N kilometers from the starting point of the highway. Given a possible choice for the branches, we define its balancing has the minimal distance between any two branches chosen (where the distance between two cities is calculated as the difference of the relative K_i, K_j). What is the maximum possible balancing for a choice of F branches among the N given cities?