What is the relation between the two main problems arising from vagueness, the Sorites paradox and the Problem of the Many? This question seems to be neglected. In explaining this relation, this paper shows that the usual understanding of these problems is unsatisfying and shows what instead is fundamental to these problems. The usual understanding of the Sorites paradox is that it is a problem arising for (apparently) vague concepts, while the Problem of the Many is understood to be a problem arising for ordinary objects. This paper, however, shows that both problems can arise for any kind of phenomenon of vagueness. Instead, what is fundamental to them is \textit{the number of boundary crossings} that are involved, a novel notion introduced and further explained in this paper. Where the Problem of the Many arises for a collection of \textit{multiple} boundary crossings, the Sorites paradox arises for \textit{one} single boundary crossing.