Positive integers 1 to 9 are written in each square of a 3×3 table. Let us define an operation as follows: Take an arbitrary row or column and replace these numbers a,b,c with either non-negative numbers a−x,b−x,c+x or a+x,b−x,c−x, where x is a positive number and can vary in each operation.
(1) Does there exist a series of operations such that all 9 numbers turn out to be equal from the following initial arrangement a)? b)?
a)147258369)
b)296837541)
(2) Determine the maximum value which all 9 numbers turn out to be equal to after some steps. combinatorics proposedcombinatorics