The problem considered in this paper arose in the study of the radiation properties of smoke and fog. In the first approximation, these are sols consisting of absolutely black particles. The transparency of the layer can be characterized by the value of the average area in the flow cross-section perpendicular to the line of sight, not covered by sol particles. This point of view belongs to K. S. Shifrin. The need arises to solve the following question: what is the average value of the free area of a limited piece of a plane when n "elementary" regions are located on it, closed and congruent (such an assumption means that a monodisperse sol is considered).
