In the paper  the determinant criterion of solvability for the Kuczma equation  was given. This criterion appeared in the natural way as barycenter of some mass system. It turned out that determinants do appear in many different situations as solvability criteria. The present article is aimed to review the mostly classical results in the theory of functional equations from this point of view. We begin with classical results of the linear functional equations and the determinant equations solved by F. Neuman. Using natural hierarchy we select some class of well-known equations in order to catch a pattern in the solvability criteria. This approach gives some sort of hypothesis.