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From: pace@othervax.UUCP
Newsgroups: net.math
Subject: Yet Another Puzzle
Message-ID: <313@othervax.UUCP>
Date: Wed, 22-Aug-84 13:03:52 EDT
Article-I.D.: othervax.313
Posted: Wed Aug 22 13:03:52 1984
Date-Received: Thu, 23-Aug-84 07:45:49 EDT
Organization: Micom Co., Montreal Canada
Lines: 29

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What we have here is a problem one of my lecturers back in the 
good old days gave me:

Please forgive me if you've all seen this before but I havn't 
been reading net.math for very long. Anyway, here it is;

for ANY POSITIVE integer, call it "i", will the following 
"program" ALWAYS (eventually!) stop ?

step 1:   if( i == 1 ) then STOP;
step 2:   if( i is even ) then  i = i/2  else  i = 3*i + 1;
step 3:   go to step 1;

We do of course assume that 'i' can be infinitely large etc.

Well, what do you think, can any of you give a proof showing that
it will stop (or halt or exit, whatever) for any positive
integer?
You will probably immediately think of the old HALTING problem
we all learned about back in school.

Well, if you want to know whether it can be done or not (that's
if you already havn't guessed it by now), drop me a line and 
I'll tell you.

cheers ,   Scott Pace, Micom Co., Montreal