Statement

To keep in shape after the first lockdown, Luca decided to sign up at a local swimming pool. Being a novice, he opted for a course where a professional trainer supervises a number of athletes to give advice while they do their lengths. Luca, however, couldn't help to notice that the position of the trainer is suboptimal and she has to continuously shout to be heard by everybody, even before the first dive. The N athletes are in fact starting at different positions P_i (from 0 to N-1), seen from left to right and measured in centimeters from the left wall of the pool. The trainer always chooses to stay exactly behind one of them, i.e. she selects a position P_t that coincides with that of one of the athletes. In this way, she is exactly 0 centimeters away from one athlete, but potentially very distant from some of them...