Yeah, I think you nailed it. the spacing issue is just a red herring, once a dime is in the center, point symmetry can be used inductively to show any valid placement will guarantee a the point symmetric opposite position will also be valid!

hmmmm, so I need to keep away from the trivial ones...

4 ants standing on the corners of a 1 foot square begin walking directly towards the ant clockwise from themselves at the same moment at the same speed, thus spiraling inward as the go. How far will each have walked by the time they meet?

(got another for me?)