greg@uwvax.ARPA (Greg Johnson) (07/29/83)
Regarding Mark Brader's submission about the "Sally/Paul" problem, the pair (4, 13) is indeed a solution to the problem that appears in Mathematics Monthly and Scientific American (see below for exact references). However, the problem that appeared in net.math and is repeated by Mark Brader is different, and has a different solution. The problem in Math. Monthly is as follows: Let x and y be two integers with 1 < x < y and x + y <= 100. Suppose Sally is given the value of x + y and Paul is given the value of xy. 1) Paul says, "I don't know the values of x and y." 2) Sally replies, "I knew that you didn't know the values." 3) Paul responds, "Oh, then I do know the values of x and y." 4) Sally exclaims, "Oh, then so do I." The problem submitted to the net and repeated by Mr. Brader is: -------------------------------------------- I have picked two integers between 3 and 100 (inclusive), and given their sum to Sally and their product to Paul, both very clever mathematicians. After suitable time for thought, Sally says to Paul: "It is impossible for you to figure out my sum." After more time for thought, Paul replies: "I have figured out your sum." After still more thought, Sally says: "I have figured out your product." What are the two numbers? -------------------------------------------- The solution I submitted to the net a while back was (13, 16) (if anyone is interested, I can mail them my explanation or re-submit it to the net). This solution differs from the one that appears in Mr. Brader's article. In fact, (4, 13) cannot be the solution to the net version of the problem, since 52 factors uniquely if we restrict ourselves to integers from 3 to 100 inclusive. Paul would have known the sum immediately after being told the product. - Greg Johnson U. of Wisconsin - Madison References: Mathematics Magazine, March 1976 (vol 49 #2), page 96, Mathematics Magazine, November 1977 (vol 50 #5), page 268. Scientific American, Dec. 1979, March 1980, May 1980.