numbers in mxn board, 2 operations available, can all numbers become -1?
Source: 2020 1st Memorial Mathematical Contest "Aleksandar Blazhevski-Cane" p2
April 30, 2021
combinatorics
Problem Statement
One positive integer is written in each square of the board. The following operations are allowed :
(1) In an arbitrarily selected row of the board, all numbers should be reduced by .
(2) In an arbitrarily selected column of the board, double all the numbers.
Is it always possible, after a final number of steps, for all the numbers written on the board to be equal to ?
(Explain the answer.)