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From: lizs@munnari.OZ (Liz Sonenberg)
Newsgroups: net.math
Subject: Re: Lists of points clarification
Message-ID: <614@munnari.OZ>
Date: Thu, 20-Dec-84 03:11:33 EST
Article-I.D.: munnari.614
Posted: Thu Dec 20 03:11:33 1984
Date-Received: Mon, 24-Dec-84 03:10:30 EST
References: <206@cmu-cs-g.ARPA>
Organization: Comp Sci, Melbourne Uni, Australia
Lines: 27

> >> 	It seems to me that I must be missing something because 
> >> this looks easy. If I understand it correctly we are asked to
> >>
> >>		Greg Rawlins.
> 
> ... solve a rather ill-stated problem.  Here is a more precise formulation:
> 
> Suppose we call a list of points ( p_1, p_2, ... , p_n ) in [0,1)
> *evenly distributed* if each segment of the form [i/n,(i+1)/n) for 0<=i contains a point in the list.
> 
> The problem asks for a list of points ( p_1, p_2, ... , p_n ) such that
> ( p_1, p_2, ... , p_k ) is an evenly distributed list for *every* k between
> 1 and n, inclusive.  What is the largest n for which one can find such a list?

  I still don't see the problem.  After an *evenly distributed* list of k points
has been chosen, exactly  k  of the subintervals
[0, 1/(k+1) ),  [1/(k+1), 2/(k+1)), ... , [ k/(k+1), 1)  will contain one of
the chosen points.  By the pigeon-hole principle, there must be an interval
[i/(k+1), (i+1)/(k+1)) that doesn't contain one of the points.   Choosing the
(k+1)th  point in this interval will produce an *evenly distributed* list of
k+1  points, won't it ?   Since the first point can be chosen arbitrarily to
get an *evenly distributed* list of  1  point, it seems to me that the list
can be made arbitrarily large.

				David Wilson