When repainting a square with sizes 2x2, consisting of k black and (4-k) white cells, we will get (4-k) black and k white cells. That is why the number of black cells will change to (4-k)-k= 4-2k, that is, even number. Taking into account a fact that evenness of number of black cells does not change, from initial 32 black cells we won’t be able to get one black cell.