How to arrange $n$ points to make sure that they determine an odd number of slopes?
I was thinking to break this into the case where $n$ is even and odd. If $n$ is even then we put a line through $n-2$ points (with different slopes) and for the last two we put a line through both, since for two points there is always a line going through them.
If $n$ is odd, just take a line through each of these (with different slopes) to get an odd number of slopes.
Am I in the right path? Is this correct?