How to approach more Puzzle-like problems (octagon, intersection points)

Question

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.

Answer 1

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.