Challenge 257: The Mathemagician
Joseph is an apprentice Mathemagician. He wants to show you a new trick.
First, he asks you to pick a three-digit number. You pick a number between 100 and 999 at random, with all possibilities equally likely.
Then he tells you to reverse the digits of your number and add this to your original number. Finally, he asks you to tell him the final total. You do this.
What is the probability that he can discover your number with 100% certainty? If he guesses a number at random from the options that would lead to the same results as yours, what is the probability that he gets it right?