Bent octagon

[bonanova]

A convex octagon completely contains all 28 of its diagonals. But if you move the vertices around you can make portions of some, but not all, of them pass through its exterior. What is the largest number of such diagonals? Equivalently, how many diagonals of an octagon must remain totally in its interior?

[plasmid]

For the sake of kicking this off, and without proof of optimality, I'll say this is the best I can come up with for now.

Out of the 28 diagonals, 8 form the perimeter and are therefore out of play so to speak. Of the remaining 20, this has 5 interior and 15 (completely) exterior.

[bonanova]

For the sake of kicking this off, and without proof of optimality, I'll say this is the best I can come up with for now.

Hidden Content

Right on. I meant to say 20 diagonals. But you understood the other eight are perimeter edges.