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Further Remarks on the Jeep Problem

  • Ute Brauer
  • Wilfried Brauer
Conference paper

Abstract

The classical jeep problem (see [Fin], [Phi], [Gal]) is to compute how far a jeep can go when starting at a dump with n cans of gasoline, provided that it needs 1 canful to drive 1 unit distance and it is allowed to carry 2 canfuls of gasoline (including the contents of its tank). The optimal solution algorithm (see [Gal]) assumes that arbitrary fractions of a canful can be put into the tank. Since this seems to be a bit unrealistic, a discrete variant was considered by D. Wood in [Woo]: It is only allowed to refill the tank, when it is empty and then 1 canful has to be filled in (thus 1 can can be transported). The following solution was proposed in [Woo]: With one canful transport n − 1 cans to the next dump and go on recursively. This gives the distance function f w (n) = 1 + 1 + 1/3 + 1/5 + ... + 1/(2n − 3). It seemed to be the natural adaptation of the classical optimal solution.

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References

  1. [Bra]
    Brauer, U., Brauer, W.: A new approach to the jeep problem, EATCS Bulletin 38 (1989) 145–153Google Scholar
  2. [Fin]
    Fine, N.J.: The jeep problem, Amer. Math. Monthly, 54 (1947) 24–31CrossRefGoogle Scholar
  3. [Gal]
    Gale, D.: The jeep once more or jeeper by the dozen, Amer. Math. Monthly, 77 (1970) 493–501CrossRefGoogle Scholar
  4. [Phi]
    Phipps, C.G.: The jeep problem, A more general solution, Amer Math. Monthly, 54 (1947) 458–462CrossRefGoogle Scholar
  5. [Woo]
    Wood, D.: Paradigms and Programming with PASCAL, Computer Science Press, Rockville, 1984.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Ute Brauer
    • 1
  • Wilfried Brauer
    • 1
  1. 1.Institut für InformatikTechnische UniversitätMünchen 2Germany

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