def get_move(old_i, new_i):
    """
    Returns a string corresponding to the move between two positions of a tile
    
    old_i: a tuple representing the old index of the tile
    new_i: a tuple representing the new index of the tile
    """
    
    dx = new_i[0] - old_i[0]
    dy = new_i[1] - old_i[1]

    if dx > 0:
        return "left"
    elif dx < 0:
        return "right"
    elif dy > 0:
        return "up"
    elif dy < 0:
        return "down"
    else:
        return ""