You arrive for a meeting and have to sit at a large round table at which three people you violently dislike are already seated. Where should you place your chair so that, when you add up the shortest distances round the edge of the table from yourself to each of these "nasties", the total distance you get is as large as possible? (Of course since the nasties are already seated you have no control over their location.)

Hint 1

What happens to the total distance if you shift your chair a little to the left or a little to the right?

Drawing of Round Table and Nasties

Hint 2

It makes a difference where the Nasties are seated relative to your centerline. Divide the problem into several cases.

Drawing of Round Table and Nasties with centerline

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