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The jeep problem is a problem about a jeep (or some other vehicle) that must cross a certain distance with a limited fuel tank.
A jeep is currently at a fuel station, and it must cross a desert that is 5 leagues long. The jeep can only carry 1 unit of fuel at a time, and each unit of fuel will allow the jeep to travel 1 league.
Obviously, the jeep cannot cross the desert in one trip, but the driver is able to leave any amount of fuel behind to be picked up later. Thus, the driver's strategy is to travel some distance, leave some fuel behind, then return to the fuel station to get more fuel and hope to travel further with the fuel that was left behind on previous trips.
What is the minimum units of fuel the driver must purchase to cross the desert?
There are other variations of the problem, but they generally follow the same premise. The jeep problem's solution is related to harmonic numbers.