Question 54
Triangular lattice cuts an equilateral triangle with a side of length $n$ into $n^2$ triangular cells (Fig. 1). Some of the cells are infected. A cell, which is not infected yet, could be infected if it is neighbouring (by side) with at least two already infected cells. Determine the minimal amount of initially infected cells such that eventually every cell in the triangle could get infected if $n = 12$.
Fig. 1
Fig. 1