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From: verma@ucla-cs.UUCP
Newsgroups: net.math
Subject: Re: Counter-Intuitive Sequences
Message-ID: <8675@ucla-cs.ARPA>
Date: Sun, 2-Feb-86 07:47:25 EST
Article-I.D.: ucla-cs.8675
Posted: Sun Feb  2 07:47:25 1986
Date-Received: Tue, 4-Feb-86 03:24:50 EST
References: <748@garfield.UUCP>
Reply-To: verma@ucla-cs.UUCP (Thomas S. Verma )
Organization: UCLA Computer Science Department
Lines: 23
Keywords: jumping to conclusions

In article <748@garfield.UUCP> robertj@garfield.UUCP (Robert Janes) writes:
>Consider the following sequence:
>
>		1, 2, 4, 8, 16,....
>
>what is the next term ?	
>
>Invariably the response is "32".
>This however does not have to be the case and an alternate sequence arises
>very naturally. Consider the sequence of n where n is the number of regions
>the interior of a circle can be divided into using k lines where k starts
>at 0. If you do that for the first five k you get the above sequence.
>Suggestive isn't it ? However it turns out that for k=6 n=31 and the 
>intuitive result falls flat on its face.

I do not understand what you mean.  I drew a circle.  I saw one region.
I then drew a chord.  I saw two regions.  I drew another chord.  I saw
four regions.  Now the third chord could go in two non-isomorphic places.
One gave six regions, the other gave seven.  No matter how hard I tried,
I could not get eight.  With four I could get as high as eleven, not
thirty-two.  Please tell me what you are talking about...

						TS Verma