I have a pet ant that I keep on a leash. I keep her on the outside surface of a cube. Her leash is twice the length of an edge of the cube. I'm trying to decide where to attach the leash.

A: At a vertex.

B: At the center of an edge.

C: At the center of a face.

Which choice gives my pet ant the most area to roam?

(In reply to Some Trouble (possible solution) by Daniel)

After reading Charlie's solution I see where my logic failed, while using the grid was the proper start to the solution, what I failed to take into account is that in the grid representation each face of the cube is represented by multiple grid squares.  Thus those duplicates would have to be ignored when looking at the circle drawn and this is what leads to the different total areas.

Posted by Daniel on 2018-09-01 04:19:17