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From: makaren@alberta
Newsgroups: net.puzzle
Subject: S and P (REPEAT AGAIN)
Message-ID: <557@alberta.UUCP>
Date: Sun, 13-Nov-83 19:57:37 EST
Article-I.D.: alberta.557
Posted: Sun Nov 13 19:57:37 1983
Date-Received: Tue, 15-Nov-83 20:05:08 EST
Organization: U. of Alberta, Edmonton, AB, Canada
Lines: 30

I have received some mail about this puzzle having been garbled at some
  sites and so I am posting it a third time.  Appologies included.
  Maybe if I include enough
  lines of text at the
  beginning of the message
  then the puzzle will not
  end up garbled.
  I have also removed the
  first blank line in the hopes that this will
  have some effect.
  Anyway here is the puzzle again. ----
     There are two mathematicians which we will call "S" and "P".
     They are in a contest.
     The judge of the contest chooses two integers tells the mathematicians
         "Both integers are greater than one"
         "The sum of the two integers is less than forty"
         "The product of the two integers is less than four hundred"
     The judge then writes down the sum of the two integers and gives
     it to mathematician "S". He then writes down the product of the 
     two integers and gives it to mathematician "P".
     He then instructs both mathematicians to determine both the 
     sum and product of the two integers.
     After considerable thought mathematician "S" says to mathematician "P"
        "There is no way that you can determine the sum"
     Mathematician "P" replies "Then I know the sum"
     Mathematician "S" responds "Then I know the product"

  YOUR PROBLEM: What were the two integers?
  note: We assume that mathematicians do not make mistakes in matters of logic.
   I will post the solution at a later date if nobody solves it.