2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35732Paradoxes that can supposedly occur if a time machine is created are discussed. It is shown that the existence of trajectories of ``multiplicity zero'' (i.e. trajectories that describe a ball hitting its younger self so that the latter cannot fall into the time machine) is not paradoxical by itself. This {\em apparent paradox} can be resolved (at least sometimes) without any harm to local physics or to the time machine. Also a simple model is adduced for which the absence of {\em true} paradoxes caused by self-interaction is proved.9 LaTeX pages, 23k. bezier.sty is desirable, but its absence will only damage two figuresGeneral Relativity and Quantum Cosmologytext