Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/5/84; site rochester.UUCP Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!decvax!genrad!wjh12!harvard!seismo!rochester!FtG From: FtG@rochester.UUCP Newsgroups: net.math Subject: odd-sided polyhedral dice Message-ID: <892@rochester.UUCP> Date: Tue, 25-Sep-84 08:19:31 EDT Article-I.D.: rocheste.892 Posted: Tue Sep 25 08:19:31 1984 Date-Received: Thu, 27-Sep-84 05:16:02 EDT Sender: FtG@rochester.UUCP Organization: U. of Rochester, CS Dept. Lines: 16 From: FtG alice!td asks if there exists fair odd-sided polyhedral dice for all odd m=2n+1>=5. The following is an existence proof. Consider a 2n sided pyramid with all sides identical and consider varying the size of the base. If the base is extremely large, then that side will be favored. If the base is extremely tiny, then the sides will be favored. Clearly this is a continous deformation with a resulting continous function of the probability of landing on the base vs one of the sides. Ergo there exists a point where the probabilities are equal, QED. Note this is not constructive, but "I do and I do and I do for you kids and this is the thanks I get?" FtGone