Overriding Methods challenge - the code below works perfectly for me in Xcode 9.2 but keep getting 'code won't compile'

The reason why it complains about the code not compiling is that firstName and lastName are declared with let, which makes them constants. That means that it's invalid to change their contents after they are assigned a value, which they are when you call the super.init method.

Are you sure you tried that exact code snipped in Xcode? In theory it should not work in any Swift compiler. If you declared firstName and lastName with var like this:

class Person {
  var firstName: String
  var lastName: String 

  init(firstName: String, lastName: String) {
    self.firstName = firstName
    self.lastName = lastName
  }

  func fullName() -> String {
    return "\(firstName) \(lastName)"
  }
}
// Enter your code below
class Doctor: Person {
    override init(firstName: String, lastName: String) {
        super.init(firstName: firstName, lastName: lastName)
        self.firstName = "Dr."
    }
}
let someDoctor = Doctor(firstName: "Sam", lastName: "Smith")

Then your code should compile, and in fact that code passes the challenge fine.

But one thing you should note for future reference is that challenges, as a general rule, are pretty strict about their instructions. If they ask you to do a specific thing in your code, then doing anything besides that thing will usually fail, even if the result of your code ends up being what the challenge asks for.

So while the code above (which is not really what the challenge asked you to write) does pass this particular challenge, it is rarely the case that challenges are so lenient. In most cases you have to follow the instructions to the letter. Practically any deviation from the template answer the challenge was programmed with tends to get your code invalidated.