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Path: utzoo!linus!decvax!mcnc!ncsu!ncvet!mtj
From: mtj@ncvet.UUCP (Michael Jones)
Newsgroups: net.games,net.math,net.puzzle
Subject: Solution to DSR Contest Announced
Message-ID: <130@ncvet.UUCP>
Date: Tue, 30-Oct-84 16:30:46 EST
Article-I.D.: ncvet.130
Posted: Tue Oct 30 16:30:46 1984
Date-Received: Thu, 1-Nov-84 03:24:33 EST
Organization: N.C. State University Vet School, Raleigh
Lines: 63



The first Data Systems Research, Inc. contest has been won by Fred Helenius
of Boston, MA.	His winning entry was postmarked October 17, 1984.  Quite a
few entrants failed to find the proper solution, and none appeared aware of
the name for this sequence.

The information given in the contest announcement was:

   1. The following four numbers are part of a much longer sequence.

		     54748

		     92727

		     93084

		    548834

   2. They appear in this longer sequence consecutively.

   3. They appear in this longer sequence in the order given (top to bottom).

   4. Each number appears only once in the longer sequence.

   5. The longer sequence consists of numbers with a special property.

   6. The longer sequence is finite.

The questions asked were:

   1. What two numbers (if any) preceed 54748 in the longer sequence ?

   2. What two numbers (if any) succeed 548834 in the longer sequence ?

   3. What special property do these numbers possess ?

The answers are:

   1. 8208 and 9474 preceed 54748 in the longer sequence.

   2. 1741725 and 4210818 succeed 548834 in the longer sequence.

   3. These numbers are n-digit numbers which are equal to the sum
      of the n-th powers of their digits.

Some numbers in this sequence are:

       153 = 1^3 + 5^3 + 3^3
      8208 = 8^4 + 2^4 + 0^4 + 8^4
     54748 = 5^5 + 4^5 + 7^5 + 4^5 + 8^5
    548834 = 5^6 + 4^6 + 8^6 + 8^6 + 3^6 + 4^6
   4210818 = 4^7 + 2^7 + 1^7 + 0^7 + 8^7 + 1^7 + 8^7

A very large number with this property is:

   128468643043731391252 = 1^21 + 2^21 + 8^21 + ... + 5^21 + 2^21

This first Data Systems Research, Inc. contest has been fun for us,  and
for the many of you who entered.  The second contest will begin soon. It
will be announced on the net, as well as on personal RBBS systems.