MathDB

All the numbers

1,2,...,9

are written in the cells of a

3\times 3

table (exactly one number in a cell) . Per move it is allowed to choose an arbitrary

2\times2

square of the table and either decrease by

1

or increase by

1

all four numbers of the square. After some number of such moves all numbers of the table become equal to some number

a

. Find all possible values of

a

.
I.Voronovich

Problem Statement