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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