Question 84
Let $n \gt 1$ be an integer and let an $2 \times n$ grid be given, where the cells are labelled as $(x, y)$ with $1 \le x \le 2$ and $1 \le y \le n$. A grasshopper lives on the grid and occasionally jumps from one cell to another. The *length* of a jump from a cell $(x_1, y_1)$ to $(x_2, y_2)$ is defined as $|x_1 - x_2| + |y_1 - y_2|$. Determine the largest possible sum of lengths of jumps the grasshopper can make when it starts from one cell and never jumps to a cell it has visited before.