A javascript solution to a simple practice problem

robotPaths.js

/**
 *
 *  A robot located at the top left corner of a 5x5 grid is trying to reach the
 *  bottom right corner. The robot can move either up, down, left, or right,
 *  but cannot visit the same spot twice. How many possible unique paths are
 *  there to the bottom right corner?
 *
 *  make your solution work for a grid of any size.
 *
 */

// A Board class will be useful

var makeBoard = function(n) {
  var board = [];
  for (var i = 0; i < n; i++) {
    board.push([]);
    for (var j = 0; j < n; j++) {
      board[i].push(false);
    }
  }
  board.togglePiece = function(i, j) {
    this[i][j] = !this[i][j];
  };
  board.hasBeenVisited = function(i, j) {
    return !!this[i][j];
  };
  return board;
};

var robotPaths = function(n, board, i, j) {
  // Initialize these if not provided
  if (!board) {
    board = makeBoard(n);
    i = 0;
    j = 0;
  }
  // No possible paths if you’re off the board
  // or on a piece you shouldn’t be on
  if (!(i >= 0 && i < n && j >= 0 && j < n) || board.hasBeenVisited(i, j)) {
    return 0;
  }
  // One possible path if you’re at the
  // end point (the path that led there)
  if (i === n - 1 && j === n - 1) return 1;
  board.togglePiece(i, j);
  var result =
    robotPaths(n, board, i, j + 1) +
    robotPaths(n, board, i, j - 1) +
    robotPaths(n, board, i + 1, j) +
    robotPaths(n, board, i - 1, j);
  // Return the board to its original state
  board.togglePiece(i, j);
  return result;
};

console.log(robotPaths(6));