MathDB

Cells of a

n*n

square are filled with positive integers in the way that in the intersection of the

i-

th column and

j-

th row, the number

i+j

is written. In every step, we can choose two non-intersecting equal rectangles with one dimension equal to

n

and swap all the numbers inside these two rectangles with one another. ( without reflection or rotation ) Find the minimum number of moves one should do to reach the position where the intersection of the

i-

th column and

j-

row is written

2n+2-i-j

Problem Statement