(a) If an ant is placed on each vertex of a regular isocagon, what is the probability that there will be no encounter between any two ants if all ants start moving simultaneously and randomly (either clockwise or anti-clockwise) along the edge to the next vertex without changing direction?
What are the chances of no encounter if there are …
(b) Four ants, each placed on the vertices of a tetrahedron?
(c) Eight ants, starting at the corners of a cube?