"A piece of land of a square shape with dimensions 10m x 10m is divided into 100 square parcels with dimensions 1m x 1m. Initially, 9 of the parcels are overgrown by weed. If a parcel is surrounded by at least 2 parcels with weed from its sides after some time that parcel will be overgrown by weed. Can the whole piece of land grow into weed after some time?"
This is what I'm trying to solve in a math essay. I was able to prove that the whole piece of land won't grow into weed by monitoring the changes in perimeters (e.g. two parcels with a perimeters of 8 unit can only results in shapes with a perimeter of 8 units. Therefore 9 parcels (36 units of perimeter) can not turn the whole field (40 units of perimeter) into weed.
Another similar approach would be monitoring the "points" along the perimeter, but that is basically the same way of solving.
Can this question be solved in any other ways? If possible, could you give me some hints? (not the whole idea pls because I want to do this by myself).