There are $n$ gas stations located on a circular route. Together they contain exactly enough gas to make one trip around.
Prove that there exists a gas station (say $A$), such that if you start at $A$ with an empty tank you can travel around the circular route and come back to $A$ without running out of gas.
Moreover, prove that if there is enough gas in total to make two rounds, then there is a gas station from where you can travel around both clockwise and counterclockwise.
Moreover, prove that if there is enough gas in total to make two rounds, then there is a gas station from where you can travel around both clockwise and counterclockwise.
domotorp (Jun 24 '12)edit@domotorp Cool extension.
Shiva Kintali (Jun 24 '12)edit