Chessboard, Tiling, Maths A square-shaped garden is divided into an n x n square grid by footpaths (like a chessboard). 

The owner wishes to have all the sections covered by grass; however, the grass grows in a peculiar way. If at least two of the neighbouring squares (i.e. squares that share an edge) of a given square become fully covered with grass, then so will the given square. 

What is the minimum number of squares that need to be planted initially so that the grass will eventually extend to the whole garden?
The solution in the book (see my comment on the original question) is terrific: just note that the perimeter of the grassy region never increases.
Take $2*2$ case, and plant grass in diagonal squares initially this will cover complete 4 squares. Now add 5 squares along adjacent edges of given square to make it a $3*3$ square. No squares of the newly added squares grow grass on its own. So you need to plant one square, any square of the newly added squares with grass and you are done. This logic can be extended to higher $n$. Thus minimum square need to be planted with grass initially is $n$.