Math help, please. Here’s the problem.

You have a circle with a diameter of 80 miles. You have 100 points somewhere on or in that circle. You need to travel to all 100 points. You can start at any point and don’t need to return there – when you reach the last point you’re done. You want to travel as short a total distance as possible (or something close to that) as you travel to all 100 points.

Is it possible to calculate the maximum distance which would be the shortest route to all 100 points? And is it possible then to calculate the highest possible average distance traveled between points?

Here’s what I did, I don’t know if this is right. The diameter = 80. Set pi as 3.15 for the sake of cleaner numbers. The circumference then is 252. I could be wrong, but I think the largest possible distance would if you had 99 points around the circumference and 1 at the center. You would travel the circumference, 252 miles, then travel 40 miles to the center (or travel from the center to some point on the circumference then travel the circumference) for a total of 292 miles. In that case, you travel an average of 2.92 miles between points.

Did I make a mistake here?

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