How to approach more Puzzle-like problems (octagon, intersection points) In physics I understand the situation and can derive formulas to describe it. But when it comes to more puzzle-like math problems like this: 
"All 20 diagonals are drawn in a regular octagon. At how many distinct points in the interior of the octagon (not on the boundary) do two or more diagonals intersect?"
Although trivial, I always get stuck. I don't know how to approach it. What do you do when you encounter problems like these? Could you describe the process? Where can I find problems to improve my skill? In class we are always given the formulas and the tests consists of braindead plugging and chugging. 
 A: Some ideas: 


*

*Look for symmetries and conditions that always hold (in a triangle, the three median lines always meet at a common point), 

*See what you can learn by solving a simpler version of the problem (e.g. a regular pentagon) 

*Download or buy Georg Polya's "How to Solve It" book. There are many gems within this book, and it even addresses some non-mathematical puzzles.

A: There is no universal approach to solve this sort of puzzle problems. Every problem is different. You just have to bang your head against the wall at them for a while, and hope this improves the chances of something going in when you finally give up and look at the solution. Over time you pick up ideas and learn to apply them to similar problems.
For this particular problem I suggest you consider Euler's formula: For any planar graph with exactly $F$-many faces, $E$-many edges and $V$-many vertices we have that $F-E+V=1$. 
The question describes a graph and then asks for the value of $V$. So if we can find $F$ and $E$ we're done! Is it any easier to figure out those values from the description?
