Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/5/84; site ssc-vax.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxj!ihnp4!drutx!houxe!hogpc!houti!ariel!vax135!cornell!uw-beaver!ssc-vax!skrivan From: skrivan@ssc-vax.UUCP Newsgroups: net.puzzle Subject: Sums of Subsets Problem Message-ID: <157@ssc-vax.UUCP> Date: Wed, 17-Oct-84 12:19:48 EDT Article-I.D.: ssc-vax.157 Posted: Wed Oct 17 12:19:48 1984 Date-Received: Sun, 21-Oct-84 13:53:18 EDT Distribution: net Organization: Boeing Aerospace Co., Seattle, WA Lines: 27 The following is a problem I have been carrying along for many years with little or no progress. As I reach the prime years of my life I want to know this problem's secret (from me) solution. Help! PROBLEM: Consider a set N of n positive integers with largest element X. There are m = 2**n subsets (empty set included). Form the m sums of elements of these subsets. What is the set N with smallest X such that the m sums are unique? The following are some of the known solutions: n set _ ___________________ 1 {1} 2 {1,2} 3 {1,2,4} and {2,3,4} 4 {3,5,6,7} 5 {6,9,11,12,13} As n increases, candidate sets N can be constructed with unique sums of subsets. However, I don't know if they are the solution sets. Of course, I would prefer a mathematical solution for the general case. Jim Skrivan