Maresin $B$.

One of the simplest multicellular organisms - the algae volvox - represents a spherical shell, mainly composed of heptagonal, hexagonal, and pentagonal cells (i.e., cells having seven, six, or five neighbors; at each "vertex," three cells meet). There are specimens with quadrilateral and octagonal cells, but biologists have noticed that if such "non-standard" cells (with fewer than five or more than seven sides) are absent, then the number of pentagonal cells is 12 more than the number of heptagonal cells (the total number of cells can be several hundred or even thousands). Can you explain this fact?
The statement of the problem follows from Euler's formula. (For Euler's formula, see "Kvant" #4, 1972 or Courant and Robbins "What is Mathematics?" M., "Prosveshcheniye", 1967). Indeed, let the number of vertices of the volvox be denoted by $B$, the number of edges by $P$, and the number of faces with $i$ vertices by $\Sigma_{i}$. Then, by Euler's formula,

$$
2=B-P+\Sigma \Gamma_{i} .
$$

But $3 B=\Sigma_{i} \Gamma_{i}$, since, by condition, three faces meet at each vertex, and $2 P=\Sigma_{i} \Gamma_{i}$ - each edge is adjacent to two faces. Therefore,

$$
12=6 B-6 P+6 \Sigma \Gamma_{i}=\Sigma 2 i \Gamma_{i}-\Sigma 3 i \Gamma_{i}+\Sigma_{6} \Gamma_{i}=\Sigma(6-i) \Gamma_{i} \text {. }
$$

By condition, there are no non-standard faces, i.e., $\Gamma_{3}=\Gamma_{4}=\Gamma_{8}=\Gamma_{9}=\ldots=0$. Therefore, $\Gamma_{5}-\Gamma_{7}=12$ - in remarkable agreement with the observations of biologists.