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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