A (2n+1)×(2n+1) grid, with n>0, is colored in such a way that each of the cell is white or black. A cell is called special if there are at least n other cells of the same color in its row, and at least another n cells of the same color in its column.(a) Prove that there are at least 2n+1 special boxes.
(b) Provide an example where there are at most 4n special cells.
(c) Determine, as a function of n, the minimum possible number of special cells. functioncombinatorics unsolvedcombinatorics