Question 92
On a ball-shaped planet $X$ there are $2n$ gas stations. Each station is paired with exactly one other station, and any two paired stations are located at diametrically opposite points of the planet. Each station holds a certain amount of gasoline. The following is known: if a car with an initially empty (sufficiently large) tank starts from any station, it can always reach the station paired with it (possibly refuelling at other stations along the way). Determine all natural numbers $n$ such that, for any arrangement of $2n$ stations satisfying the stated condition, there always exists a station from which a car with an initially empty tank can start and visit all the other stations on the planet. (Assume that the car consumes a constant amount of gasoline per unit length.) (Nikola Petrović)