MathNet 1997 — Part 01 Question 34

To make a complete lap in a car around a circular circuit, the exact amount of gasoline is distributed in fixed tanks located at any $n$ different points of the circuit. Initially the car's tank is empty. Demonstrate that whatever the distribution of fuel in the tanks, there is always a starting point so that a complete turn can be made.

Consumption is assumed to be uniform and proportional to distance.