MathDB

Let

n\ge 4

be an integer. You have two

n\times n

boards. Each board contains the numbers

1

n^2

inclusive, one number per square, arbitrarily arranged on each board. A move consists of exchanging two rows or two columns on the first board (no moves can be made on the second board). Show that it is possible to make a sequence of moves such that for all

1 \le i \le n

and

1 \le j \le n

, the number that is in the

i-th

row and

j-th

column of the first board is different from the number that is in the

i-th

row and

j-th

column of the second board.

Problem Statement