Question 131
In every cell of a board $101 \times 101$ is written a positive integer. For any choice of 101 cells from different rows and columns, their sum is divisible by 101. Show that the number of ways to choose a cell from each row of the board, so that the total sum of the numbers in the chosen cells is divisible by 101, is divisible by 101.
(Borislav Kirilov)
(Borislav Kirilov)