Shrager.pa@XEROX.COM.UUCP (08/14/87)
Someone here is looking for the source of an old logic problem about two people named Mr. P. and Mr. S. One of these knows the product of some numbers and the other one knows their sum. Together they can figure out the numbers. There is a particular conversation that goes on between them something like: Mr. P. I don't know the numbers. Mr. S. I knew you didn't. Neither do I. ... and they eventually figure out the numbers. The reference is for a paper going to the publisher in a few days, so if anyone can help us with an exact reference and the precise text of the conversation, it would be greatly appreciated. (Although it might be interesting to talk about the answer, and how it can be figured out, right now we're pretty desperate for a citation.) Thanks in advance. -- Jeff
luke@uicsgva.UUCP (08/20/87)
I definitely saw this problem in the "Mathematical Games" section of Scientific American some years ago. I am not sure which issue it appeared in, but I am positive that it came out between 1979 and 1982. I am 90% certain that it can be found in the range of January 1980 to December 1981. My first guess would be the October 1980 issue. The article says that the problem made its debut at a party primarily attended by mathematicians. I don't remember all the details of the problem, but here is what I do remember: Mr. P and Mr. S are experienced mathematicians. X and Y are two different positive integers (For the benefit of the reader, it has been disclosed that both X and Y are less than or equal to 20. This constraint, however, is sup- posedly unnecessary.) The sum of X and Y has been disclosed to Mr. S and the product of X and Y has been disclosed to Mr. P. Neither man knows the value of X or Y, nor are they allowed to tell the other what their sum or product is. They are allowed to talk to each other over the phone, and do so after sufficient time to think about what the other has said. The dialogue, as far as I remember is as follows: Mr P to Mr S: I can't tell from the product what X and Y are. (later....) Mr S to Mr P: I can't tell what they are either. (later....) Mr P to Mr S: I still can't tell what X and Y are. At this point, my memory fails me. But this is the earliest point that I could feel comfortable with the following dialogue. I'm pretty sure that these guys start knowing something within two more bounces. Mr ?? to Mr ??: Now I know what X and Y are. (later) Mr ?? to Mr ??: In that case, I know what X and Y are too! According to Scientific American, the answer is 4 and 13. If anyone finds the article, I would also like to know the reference. - Luke Young Computer Systems Group University of Illinois +-------------------------------------------------------------+ | BITNET : LUKE@UIUCVMD CSNET: luke%haydn@uiuc.csnet | | UUCP : {ihnp4,seismo,pur-ee,convex}!uiucuxc!uicsgva!luke | | ARPANET : luke@haydn.csg.uiuc.edu or luke%haydn@uiucuxc | | acoustic: office (217) 333-8164 home (217) 328-4570 | | physical: 6-123 CSL, 1101 W Springfield, Urbana, IL 61801 | +-------------------------------------------------------------+