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Kindly comments on Open Thread, Apr. 13 - Apr. 19, 2015 - Less Wrong Discussion

4 Post author: Gondolinian 13 April 2015 12:19AM

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Comment author: Salemicus 16 April 2015 04:19:23PM *  4 points [-]

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.

Comment author: Kindly 18 April 2015 03:29:42PM *  0 points [-]

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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