Code shared from the Rust Playground

playground.rs

// Compile with: rustc -C opt-level=3 -C target-cpu=native

const SIDE: usize = 6;
type BoardType = u64;

struct Board { squares: BoardType }

impl Board {
    fn new() -> Self {
        /*static_*/assert!(std::mem::size_of::<BoardType>() * 8 >= SIDE * SIDE);
        Self { squares: 0 }
    }

    fn toggle_piece(&mut self, i: usize, j: usize) {
        self.squares ^= 1 << (i * SIDE + j);
    }

    fn has_been_visited(&self, i: usize, j: usize) -> bool {
        (self.squares & (1 << (i * SIDE + j))) != 0
    }
}

fn robot_paths() -> usize {
    fn robot_paths(board: &mut Board, i: usize, j: usize) -> usize {
        if i == SIDE - 1 && j == SIDE - 1 {
            return 1;
        }
        board.toggle_piece(i, j);
        let mut result = 0;

        for &(s0, s1) in [(0, 1), (1, 0), (-1, 0), (0, -1)].iter() {
            let i = (i as isize).wrapping_add(s0) as usize;
            let j = (j as isize).wrapping_add(s1) as usize;
            if i < SIDE && j < SIDE && !board.has_been_visited(i, j) {
                result += robot_paths(board, i, j);
            }
        }
        board.toggle_piece(i, j);
        result
    }

    robot_paths(&mut Board::new(), 0, 0)
}

fn main() {
    println!("{:?}", robot_paths());
}