numbers in each cell of an nxn board
Source: 1976 Swedish Mathematical Competition p4
March 26, 2021
combinatoricsgridsquare table
Problem Statement
A number is placed in each cell of an 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''.