Plot of amount of fuel f vs distance from origin d for exploring (1–3) and crossing (I–III) versions of the jeep problem for three units of fuel – coloured arrows denote depots, diagonal segments denote travel and vertical segments denote fuel transfer
The jeep problem,[1]desert crossing problem[2] or exploration problem[3] is a mathematics problem in which a jeep must maximize the distance it can travel into a desert with a given quantity of fuel. The jeep can only carry a fixed and limited amount of fuel, but it can leave fuel and collect fuel at fuel dumps anywhere in the desert.
The problem first appeared in the 9th-century collection Propositiones ad Acuendos Juvenes (Problems to Sharpen the Young), attributed to Alcuin, with the puzzle being about a travelling camel eating grain.[4] The De viribus quantitatis (c. 1500) of Luca Pacioli also discusses the problem. A modern treatment was given by N. J. Fine in 1947.[1]
^ abWeisstein, Eric W. "Jeep Problem". MathWorld.
^Gardner, Martin (1994). My Best Mathematical and Logic Puzzles. Dover. pp. 53. ISBN 0-486-28152-3.
^"Exploration problems. Another common question is concerned with the maximum distance into a desert which could be reached from a frontier settlement by an explorer capable of carrying provisions that would last him for a days." W. W. Rouse Ball and H.S.M. Coxeter (1987). Mathematical Recreations and Essays, Thirteenth Edition, Dover, p32. ISBN 0-486-25357-0.
^Problems to Sharpen the Young, John Hadley and David Singmaster, The Mathematical Gazette, 76, #475 (March 1992), pp. 102–126.
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