Here are some things.

Brain teaser #1

thatintp:

Typical “stars” are drawn in connected, but not repeated, line segments. For example, a 5-point star is drawn as such - line segments AC, CE, EB, BD, DA. The segments must always alternate a constant number of points (in the above case, skipping 1 point in between). 
Given the information that there is only 1 way to draw a 5-point star, and that there is NO way to draw a 6-point star (in continuous lines, that is), and there are 2 ways to draw a 7-point star, how many different ways are there to draw a 1000-point star?

This teaser is extremely hard, and answers must have logical explanations, since it’s hard I will know if you cheat.

~A

I am thinking through this right now, and it is indeed very hard.