The elementary solutions of boundary-value problems can be briefly characterised in the following way: We may - occasionally - substitute the general, sometimes even routine-like application of differential calculus for making use of the proper inequalities taken from different domains of elementary mathematics. Since there is no "ready-made"' general method for the elementary solution, and since the number of inequalities to be taken into consideration is - so to say - unlimited, thus solving each of the problems means a new challenge, similarly to the case of geometrical constructions.