Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83; site cmu-cs-g.ARPA Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!philabs!cmcl2!seismo!rochester!cmu-cs-pt!cmu-cs-g!monta From: monta@cmu-cs-g.ARPA (Peter Monta) Newsgroups: net.math,net.puzzle Subject: A problem about lists of points Message-ID: <203@cmu-cs-g.ARPA> Date: Sun, 9-Dec-84 01:48:00 EST Article-I.D.: cmu-cs-g.203 Posted: Sun Dec 9 01:48:00 1984 Date-Received: Thu, 13-Dec-84 02:42:15 EST Organization: Carnegie-Mellon University, CS/RI Lines: 18 Xref: watmath net.math:1643 net.puzzle:497 A friend gave me this problem about a year ago, and I now know the answer, but not to my satisfaction. Consider a (bounded) line-segment. Choose point 1 anywhere on the segment. Then choose point 2 so that the first two points lie in different halves of the segment; choose point 3 so that the first three points all lie in different thirds of the segment; etc. What is the maximum number of points you can choose (before further choice becomes impossible)? It is convenient to consider a half-open segment, say [0,1[, and to regard 1/2 as belonging to the second half, 2/3 to the third third, etc. If you get an answer, and a compelling *reason* why the answer is true, I'd very much like to hear about it. Peter Monta ARPA: monta@cmu-cs-g UUCP: ...!rochester!cmu-cs-pt!cmu-cs-g!monta