MathNet 2019-part-02 — 184 problems (EN–VI) Question 183

Let $n \geqslant 2$ be an integer. Clara has a board of size $3 n \times 3 n$, similar to a chessboard. She has just invented a new piece, the leopard, which she can move as follows: by moving it one square up, one square to the right, or one square diagonally down and to the left. Clara placed her leopard on one of the squares of the board, then moved it, so that it never passes twice through the same square, until it returns to its starting square.
What is the largest possible number of moves Clara could have made in this way?