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Path: utzoo!watmath!ljdickey
From: ljdickey@watmath.UUCP (Lee Dickey)
Newsgroups: net.math
Subject: Dealing Triangular Numbers
Message-ID: <5447@watmath.UUCP>
Date: Sun, 26-Jun-83 19:28:23 EDT
Article-I.D.: watmath.5447
Posted: Sun Jun 26 19:28:23 1983
Date-Received: Mon, 27-Jun-83 00:24:29 EDT
Sender: ljdickey@watmath.UUCP
Organization: U of Waterloo, Ontario
Lines: 24

Start with several stacks of cards.
  Take one card from each stack, and with them, form a new stack.
  Repeat the above operation.

For instance, if you start with three stacks each with 2 cards,
                         2 2 2
you get
                         1 1 1 3
The next few rounds are:
                               2 4
                               1 3 2
                                 2 1 3
                                 1   2 3
                                     1 2 3
                                       1 2 3
We think that if you start with the right number of cards (a triangular
number,    k(k+1)/2  )
you always wind up with the numbers 1 2 3 ... .
If you start with anything other than a triangular number
of cards, that you wind up in a cycle.
                                          Lee Dickey
                                          ...!decvax!watmath!ljdickey
                                          ljdickey@watmath.UUCP
                                          University of Waterloo.