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From: monta@cmu-cs-g.ARPA (Peter Monta)
Newsgroups: net.math
Subject: list of points problem
Message-ID: <208@cmu-cs-g.ARPA>
Date: Fri, 28-Dec-84 07:06:50 EST
Article-I.D.: cmu-cs-g.208
Posted: Fri Dec 28 07:06:50 1984
Date-Received: Sat, 29-Dec-84 23:12:53 EST
Organization: Carnegie-Mellon University, CS/RI
Lines: 20

> Unless I've made a terribly stupid mistake in my program, the answer is 17.
> Why 17, you ask? It's obvious: 17 is the largest integer less than 18 :-).
>
>						Ed Sheppard
>						Bell Communications Research

Yes, I got 17 too.  The first solution of length 17 (lexicographic order) is
  ( 0 7/13 11/13 4/15 12/17 5/12 12/13 2/15 8/13 1/3 10/13 1/5 8/17 
    16/17 1/15 11/17 6/17 )

As to why there aren't solutions of length 18, the only feeling I have is
that there are relatively few new terms in the 18th Farey list (six, compared
with sixteen new terms at the 17th); this sort of constricts the search.

I haven't even been able to show that there isn't a sequence whose first n
terms is a solution for every n (except, of course, by computer program).

Peter Monta
ARPA: monta@cmu-cs-g
UUCP: ...!rochester!cmu-cs-pt!cmu-cs-g!monta