Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10 5/3/83; site watmath.UUCP 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.