MathDB

There is a board of

2008\times 2008

and

2008

pieces, one in each row and each column of the board. It is allowed to do one of the following movements:
a) Take two steps to the right and

10

up. b) Take two steps to the right and

6

steps down. c) Take two steps to the left and

6

steps up. d) Take two steps to the left and

10

steps down.
If the path down cannot be completed, it is skipped to the upper part along the same column and the route continues normally, similarly in the other directions. In each play you will move a checker using any of the allowed operations. Would it be possible that at some point, after a finite number of played, the pieces are located forming a square of side

44

in the upper left corner of the board and the remaining

72

are in the last row in the first

72

boxes?

Problem Statement