What's the least number of straight lines do you need to connect a random set of dots?

What's the least number of straight lines do you need to connect a random set of dots?
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Answer :

For your first question it seems logical that it depends of the number of points (dots) as well as the location of the points. As for how you get your answer, I doubt that there is an easy handy dandy formula to use. Why not just use your brain power?
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