We observe that the perimeter is monovariant: it can only decrease. The initial perimeter is at most 4 times the number of initial cells. The final perimeter is $4 \times 100$. Therefore, it requires at least 100 cells, and we can take the cells of a diagonal.
A bacterium develops on a $100 \times 100$ grid. It can infect a new cell if and only if two adjacent cells were already infected. What is the minimum number of initially infected cells required for the bacterium to spread everywhere?