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# Gas stations in a circle

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posted Jun 23 '12

Shiva Kintali
691 1 6 22
http://www.cs.princeton.e...

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.
Source: from book "Mathematical Puzzles: A Connoisseur's Collection"
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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.

(Jun 24 '12)edit

@domotorp Cool extension.

(Jun 24 '12)edit

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Posted: Jun 23 '12

Seen: 131 times

Last updated: Jun 24 '12