Some well known ontological puzzles are taken to show that the ontology of the familiar world is not correctly described by mereology. The usual formulations of Tibbles puzzle are here analyzed in a general and abstract way and a non usual solution of the puzzle is provided. It consists of denying the existence at a time of an entity that exists at another time, i.e. of denying certain persistence statements. A general solution of this kind is presented and motivated. According to this solution there is no need to give up the existence of composition, i.e. the principle that for any entities there is an entity composed by them, nor there is any need to give up uniqueness of composition, according to which the same entities compose only o...