Maximum number of acute interior angles in a hexagon. Is it possible for a hexagon (in the plane, non-convex, non-overlapping) to have $5$ acute interior angles?  It's possible for a pentagon or a hexagon to have $4$ acute interior angles.  There are related questions on this site, but they are for general $n$-gons and no one seems to have a definitive answer.  So what about just 6-gons?
Want to know what I tried?  Fine, I wore out 3 Expo markers on my whiteboard trying stuff.

Yes, it is possible to have $5$; see this figure for an example.  You can easily formalize the argument once you see it; I have left that as an exercise.

