A number is placed in each cell of an n×n board so that the following holds:
(A) the cells on the boundary all contain 0;
(B) other cells on the main diagonal are each1 greater than the mean of the numbers to the left and right;
(C) other cells are the mean of the numbers to the left and right.
Show that (B) and (C) remain true if ''left and right'' is replaced by ''above and below''. combinatoricsgridsquare table