MathDB

a) We are playing the following game on this table: In each move we select a row or a column of the table, reduce two neighboring numbers in that row or column by

1

and increase the third one by

1

. After some of these moves can we get to a table with all the same entries?
b) This time we have the choice to arrange the integers from

1

9

in the

3 \times3

table. Still using the same moves now our aim is to create a table with all the same entries, maximising the value of the entries. What is the highest possible number we can achieve?

Problem Statement