  In this paper we formulate and solve extremal problems in the d-dimensional
Euclidean space and further in hypergraphs, originating from problems in
stoichiometry and elementary linear algebra. The notion of affine simplex is
the bridge between the original problems and the presented extremal theorem on
set systems. A function related to Sperners theorem and the YBLM inequality is
also considered and its relation to hypergraph Turan problems is discussed.
