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In this puzzle Win the relay competition by selecting the longer path for competitors

There is a wordy and confusing set-up.

At the end of the question the following appears,

The basic mathematical problem can be described as follows:

Given three points A , B , and C and the circle that goes through them, find the point P on the circle that maximizes PA+PB+PC .

In the comments, I made the following suggestion

The whole story of the runners just confuses things as evidenced by the answers so far. I suggest removing the preamble and simply stating the geometrical problem as at the bottom of the question. Note: We need to know whether distance is measured in straight lines or around the circle. – chasly from UK 6 hours ago

The answer came back

This a puzzle not a math problem site - so it is presented as a puzzle. As I stated some other place - it has to be straight lines. Along the circle P is coinciding with B. – Moti 5 hours ago

Question

What do you think. To put it bluntly, who is right and who is wrong?

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  • $\begingroup$ I think the disagreement is whether it is a math puzzle or a math problem, not whether math puzzles are suitable. $\endgroup$ – f'' Aug 16 '15 at 3:49
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I think this challenge is a textbook example (put intended!) of a math problem that is not a math puzzle.

I spent a bit of time working on this challenge and got a solution much like f'''s now-accepted answer, though less clean. But, I found this solution disappointing that I continued to look for something nicer, perhaps a cleaner expression or a different method.

The solution is standard and boring. You express the function in the parameter with some geometry, set the derivative to zero, and do some algebra to solve for the parameter. It's something you'd see in a math textbook. It's not easy, but it doesn't require any insight or creativity. You just chug ahead with the usual technique. It's not much fun and it feels like work.

There are similar geometry problems that are much simplified after a clever idea. For example, the problem of the shortest path from a start point to end a point that touches a given line is much simplified by considering a reflected phantom point. Or, finding the point minimizing the total distance to three given points by balancing the "force vectors" in the respective directions. I had hope for a insight of this type to bear fruit.

Stating the problem in terms of runners rather than distances does not make this a puzzle, no more than "Sally had two apples..." does for an arithmetic problem.

I think it's important to avoid math problems being posted as puzzles. I feel like I wasted my time on this challenge looking for something nice that wasn't there. This weakens my trust in other puzzles that I might consider solving.

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    $\begingroup$ I almost didn't post my answer because I thought there must be a better way. If that was the intended one I would judge the question as off-topic, but the OP said in the comments that there is a "somewhat simpler solution". $\endgroup$ – f'' Aug 16 '15 at 15:07

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