<p>Okay, number 8 (again, let me remind you that I'm weird - but it works)! Here's what I did:</p>

<p>"4 distinct lines" - okay, I draw 4 straight parallel lines.

"no two lines are parallel" - oops can't do that, let's try 4 lines of different slopes

"no three lines intersect at the same point" - check! wait, but it's gotta intersect... and they can't all cross through the middle (like what a cardinal system on a map would look like) - so I draw a rectangle with sides of different slopes (like a lopsided 4 sided polygon)</p>

<p>"what is the total number of points of intersection?" - Okay here's the tough one. Well right now I have 4 points. Let us see if I can get any more - if not, then 4 is the maximum. Scooting one of the sides (making the polygon smaller or larger) gets me nowhere. Especially since these lines are infinitely long. What if I turned one of the sides at a different angle relative to the other side? hmmm nope, that's still 4 points. </p>

<p>Kind of like the riddle asking how you can cut a circular cake into 8 equal portions with only 3 cuts (you cut vertical and horizontal, and then cut it in 2 layers)... I just figured that if we made the polygon 3-sided, we could just "cut" the shape.</p>

<p>So I draw the triangular shape, and use the 4th line to cross 2 of the sides. Hmmm, so my total is 6 now. Pretty neat! </p>

<p>But just in case, let's see if we can get more. Can we draw a 2-sided shape, and then just use the other 2 lines to cross the lines? No, because the 2-sided shape doesn't really exist. Okay, how about if I had that extra 4th line cross all three of the sides, then it would be 7 points of intersection! Nope, because you can't a line cross all three sides of a triangle (unless it's 3D).</p>

<p>So, total = 6 maximum</p>

<p>I'm sure there is a formula for max points of intersection, but it's so subject pertaining to each problem :)</p>