Burdzy, KrzysztofDuarte, Mauricio2021-11-232021-11-232020-02Journal of the London Mathematical SocietyOpen AccessVolume 101, Issue 1, Pages 373 - 3921 February 202000246107http://repositorio.unab.cl/xmlui/handle/ria/21039We give a new and elementary proof that the number of elastic collisions of a finite number of balls in the Euclidean space is finite. We show that if there are (Formula presented.) balls of equal masses and radii 1, and at the time of a collision between any two balls the distance between any other pair of balls is greater than (Formula presented.), then the total number of collisions is bounded by (Formula presented.), for any fixed (Formula presented.) and large (Formula presented.). We also show that if there is a number of collisions larger than (Formula presented.) for an appropriate (Formula presented.), then a large number of these collisions occur within a subfamily of balls that form a very tight configuration. © 2019 London Mathematical Societyen37D50 (primary); 70F35 (secondary)Artículo