The same observations we used for chapter 1 also apply to chapter 2, we simply need to find a more compact way to create a long path with alcoves. We need a main path of about length \(40\) to make any number up to \(10{,}000\).

Here's a possible approach that fits on a \(10\) × \(10\) grid:

```
@.....#.#.
#.#.#.#...
.#.#..#.#.
.....#..#.
#.#.#..##.
...#.#.#..
.#.#.#..#.
..#...#.#.
#...#....#
..#..#.#..
```