Suppose a race track in the shape of a simple closed curve (i.e. it does not intersect itself), and suppose that distributed along it, in any way whatsoever, are N gas stations. Suppose that a race car needs L liters of gas to go completely around the track, and that the sum of the gas available at the N stations is exactly L.
Consider that the car cannot move without gas (*assume it can't travel by momentum alone, thus it MUST need gas to move*), and that it has constant mileage (consumption of gas is directly proportional to the distance the car moves, and depends on nothing else).
Prove that there exists at least one gas station such that, starting from it, the car can do a full lap.
Well, my friend, because you don't specify, i showld assume that the car could refill the full L allmoast symultaneous. so, if the N gass stations are in direct contact, the car would refill from each one without consuming much gass, and it will finish the tour.
Posted by vije
on 2004-07-05 10:34:46