A Pair in a Crowd of Unit Balls

Let F be a family of mutually nonoverlapping unit balls in the n -dimensional Euclidean space Rⁿ. The distance between the centres of A,B   F is denoted by d(A, B). We prove, among others, that if d(A, B)  <  4 and n ≥  5, then A andB are always visible from each other, that is, a light ray emanating from the surface of A reaches B without being blocked by other unit balls. Furthermore, if d(A, B)  < 2n / 2, then any small “shake’ of F can make A, B visible from each other.