To follow up the Albert, Bernard, Cheryl puzzle, I saw the following puzzle today, which I found much harder.
Two numbers a and b are between 2 and 99, inclusive. They aren't necessarily unique. Peter is given the product of the numbers, a * b. Sarah is given the sum, a + b.
Peter says, “I don’t know the numbers.”
Sarah says, “I knew you didn’t know the numbers.”
Peter then says, “I know the numbers now.”
Sarah then says, “Ah ha! I know the numbers now.”
What are the numbers?
Please rot13 any solutions.
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.
But I'm worried that my version of the puzzle can no longer be solved without brute force.
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