> Looking at the graph, I can see points along the curve, where a line would only intersect with 2 points on the curve. I always start out under this impressio

> Looking at the graph, I can see points along the curve, where a line would only intersect with 2 points on the curve. I always start out under this impression too, but then I think some more and realize that there are only two conditions where this is possible: 1. The line is vertical 2. The line is the tangent of the curve at one of the points 1 Is illegal by the rules of picking points, and for 2 I believe the tangent counts as two points, and in any case, for any arbitrary point A, there will be only three other points that will allow the line to be a tangent (one when where A is on the tangent and up to two where B is on the tangent, I believe). So once you've picked an arbitrary point, and you don't move vertically, there will be no more than three lines that don't follow the three-point rule, and every other possible line will follow the rule.