Do not follow this link unless you have better reflexes than I do; they went directly from the statement to a solution before I could look away, thus ruining the problem for me. Here is the statement, copied: X and Y are two different integers, greater than 1, with sum less than 100. S and P are two mathematicians; S knows the sum X+Y, P knows the product X*Y, and both know the information in these two sentences. The following conversation occurs: P says "I do not know X and Y." S says "I knew you don't know X and Y." P says "Now I know X and Y." S says "Now I know X and Y too!" What are X and Y? On Wed, Apr 15, 2015 at 7:01 PM, Tom Karzes <karzes@sonic.net> wrote:
Is this what you're thinking of?
http://en.wikipedia.org/wiki/Impossible_Puzzle
Tom
rcs@xmission.com writes:
This type of puzzle has been around since at least 1975. Gosper told me the S-and-P puzzle. I hope he can recall the exact details; my memory of it is fuzzed. Roughly (for flavor -- don't waste time trying to solve this): Two players, Sam & Paul. There are two numbers between 1 and 99. Sam is told the sum, Paul is told the product. Each can hear the other's answers; is a perfect logician, etc. Each is asked, in turn, if he knows the numbers. Sam: I don't know. Paul: I don't know. Sam: I don't know. Paul: Now I know. Sam: Now I know too. The puzzle is (of course) "What are the numbers?"
Rich
-------- Quoting Veit Elser <ve10@cornell.edu>:
There is a solution when the inmate is required to flip a coin, so let's stick with that more restrictive variant.
-Veit
On Apr 15, 2015, at 5:47 PM, Cris Moore <moore@santafe.edu> wrote:
Is the inmate allowed to _not_ flip any coin?
Cris
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