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 Fill 'Er Up! (Posted on 2004-06-03)
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.

 No Solution Yet Submitted by Victor Zapana Rating: 4.4000 (5 votes)

 Subject Author Date Sol vije 2004-07-05 10:34:46 Cryptic solution to Charlie's example Federico Kereki 2004-06-04 08:45:01 Different method Larry 2004-06-04 00:17:09 re(3): solution - no, your right! Danny 2004-06-03 23:08:01 re(2): solution - I don't think that proves the question Charlie 2004-06-03 22:20:26 re: solution - I don't think that proves the question Danny 2004-06-03 17:51:45 kudos due Ady TZIDON 2004-06-03 15:51:04 Another similar problem... Erik 2004-06-03 14:56:56 Big hints... - possible solution. Erik 2004-06-03 14:48:47 solution Charlie 2004-06-03 14:35:15 underlying assumption SilverKnight 2004-06-03 14:18:18 Hints for a solution Federico Kereki 2004-06-03 14:08:47

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