BG-MO 1996 Problem 3

A square table of size $7\times 7$ with the four corner squares deleted is given. [list=a] [] What is the smallest number of squares which need to be colored black so that a $5-$ square entirely uncolored Greek cross (Figure 1) cannot be found on the table? [] Prove that it is possible to write integers in each square in a way that the sum of the integers in each Greek cross is negative while the sum of all integers in the square table is positive. [/list]

size(3.5cm); usepackage("amsmath");
MP("\text{Figure }1.", (1.5, 3.5), N);
DPA(box((0,1),(3,2))^^box((1,0),(2,3)), black);