Round Trip

round trip puzzle

A problem by Hungarian mathematician Laszlo Lovász:

A track has n arbitrarily spaced fuel depots. Each depot contains a quantity of gasoline; the total amount of gas is exactly enough to take us around the track once. Prove that, no matter how the gas is distributed, there will be a depot at which an empty car can fill up, proceed around the track picking up gas at each depot, and complete a full round trip back to its starting depot.

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