  We introduce a simple method for proving lower bounds for the size of the
smallest percolating set in a certain graph bootstrap process. We apply this
method to determine the sizes of the smallest percolating sets in
multidimensional tori and multidimensional grids (in particular hypercubes).
The former answers a question of Morrison and Noel, and the latter provides an
alternative and simpler proof for one of their main results.
