MathDB

Find all positive integers

n

with the following property: It is possible to fill a

n \times n

chessboard with one of arrows

\uparrow, \downarrow, \leftarrow, \rightarrow

such that
1. Start from any grid, if we follows the arrows, then we will eventually go back to the start point.
2. For every row, except the first and the last, the number of

\uparrow

and the number of

\downarrow

are the same.
3. For every column, except the first and the last, the number of

\leftarrow

and the number of

\rightarrow

are the same.

Problem Statement