MathDB

6

Part of 1997 Spain Mathematical Olympiad

Problems(1)

n containers distribute gas to a car for a single loop along the track

Source: Spanish Mathematical Olympiad 1997 P6

7/31/2018
The exact quantity of gas needed for a car to complete a single loop around a track is distributed among nn containers placed along the track. Prove that there exists a position starting at which the car, beginning with an empty tank of gas, can complete a loop around the track without running out of gas. The tank of gas is assumed to be large enough.
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