From: Jason Holt <credentiality@gmail.com> Subject: [math-fun] transfinite epistemic logic puzzle Apologies if this has already been posted: http://jdh.hamkins.org/transfinite-epistemic-logic-puzzle-challenge/
--wow. That was spectacular. I also found on the internet this related puzzle by evan@scd.hp.com (Evan Whitney) dated January 1998, (which I have not solved): Here's a variation of Mr. P and Mr. S that I just made up. I believe the solution is unique and the problem completely defined. One logician, Mr. S, is told the sum of two integers. The other logician, Mr. P, is told the product of the same two integers. Mr. P knows that Mr. S knows the sum, and Mr. S knows that Mr. P knows the product. The following conversation ensues, you decide who is who: Mr. X: "I don't know what the two integers are." Mr. Y: "I knew you didn't know what they are." Mr. X: "I knew you knew that." Mr. Y: "This conversation could go on forever." Mr. X: "I still don't know what the integers are." Mr. Y: "Now I know what they are." Mr. X: "Now I know what they are, too." What are the two integers?