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Fill 'Er Up! (Posted on 2004-06-03) Difficulty: 3 of 5
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)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSolvije2004-07-05 10:34:46
Some ThoughtsCryptic solution to Charlie's exampleFederico Kereki2004-06-04 08:45:01
SolutionDifferent methodLarry2004-06-04 00:17:09
Some Thoughtsre(3): solution - no, your right!Danny2004-06-03 23:08:01
re(2): solution - I don't think that proves the questionCharlie2004-06-03 22:20:26
Solutionre: solution - I don't think that proves the questionDanny2004-06-03 17:51:45
Some Thoughtskudos dueAdy TZIDON2004-06-03 15:51:04
Some ThoughtsAnother similar problem...Erik2004-06-03 14:56:56
Some ThoughtsBig hints... - possible solution.Erik2004-06-03 14:48:47
SolutionsolutionCharlie2004-06-03 14:35:15
Some Thoughtsunderlying assumptionSilverKnight2004-06-03 14:18:18
SolutionHints for a solutionFederico Kereki2004-06-03 14:08:47
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