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) < 2⌈n / 2⌉, then any small “shake’ of F can make A, B visible from each other.