The next book has a lot of puzzles of this favour and also a theoretical analysis of these: R. Fagin, JY Halpern, Y Moses and MY Vardi. Reasoning about Knowledge. The "muddy children" puzzle is the most famous one. For me personally it would be interesting to see any such puzzles where one or both participants are polynomially-bounded (i.e., involving factoring). Does anybody know any? Helger On Mon, 5 Jan 2004, Scott Huddleston wrote:
I'm looking for one or more logic puzzles I've seen in the past that run something like the following:
Some core information is given to two people, possibly the sum and product of two integers or some relation thereon. Rusty memory says maybe one person is given the sum, the other is given the product.
Then two mathematicians iterate for awhile, A: I can't deduce the answer. B: Neither can I. A: I still can't deduce the answer. ...
and after a few rounds of this one of them can deduce the answer.
Can anyone supply some puzzles of this flavor? (without answer :-)
Thanks, - Scott
P.S.- The original wording was probably an ambiguous "I don't know the answer" rather than the more accurate "I cannot deduce the answer".
I don't think the puzzle(s) actually specified mathematicians, but realistically nonmathematicians are unlikely to make the necessary deductions.
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