In each square of a rectangular table of size \(M \times K\), a number is written. The sum of the numbers in each row and in each column, is 1. Prove that \(M = K\).
Fill the free cells of the “hexagon” (see the figure) with integers from 1 to 19 so that in all vertical and diagonal rows the sum of the numbers, in the same row, is the same.
Is it possible to fill a \(5 \times 5\) table with numbers so that the sum of the numbers in each row is positive and the sum of the numbers in each column is negative?