In an alternate universe, Peter and Sarah could have had the following conversation instead:
P: I don’t know the numbers. S: I knew you didn’t know the numbers. P: I knew that you knew that I didn’t know the numbers. S: I still don’t know the numbers. P: Now I know the numbers. S: Now I also know the numbers.
P: I don’t know the numbers.
S: I knew you didn’t know the numbers.
P: I knew that you knew that I didn’t know the numbers.
S: I still don’t know the numbers.
P: Now I know the numbers.
S: Now I also know the numbers.
But I’m worried that my version of the puzzle can no longer be solved without brute force.
In an alternate universe, Peter and Sarah could have had the following conversation instead:
But I’m worried that my version of the puzzle can no longer be solved without brute force.