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THE POEE ASTROLOGICAL SYSTEM

1.  On your next birthday, return to the place of your birth and, at
precisely midnight, noting your birth time and date of observation,
count all visible stars.

2.  When you have done this, write to me and I'll tell you what to do
next.

    The theorem to be proved is that if         LOOK FOR THIS
any even number of people take seats at        SNOWFLAKE -- IT       
random around a circular table bearing            HAS MAGIC
place cards with their names, it is              PROPERTIES
always possible to rotate the table                  |
until at least two people are opposite               v
their cards.  Assume the contrary.  let       [Illustration:  a
n be the even number of persons, and let        five-pointed
their names be replaced by the integers          snowflake]
0 to n - 1 "in such a way that the place
cards are numbered in sequence around
the table.  If a delegate d originally
sits down to a place card p, then the
table must be rotated r steps before he
is correctly seated, where r = p - d,
unless this is negative, in which case r
= p - d + n.  The collection of values
of d (and of p) for all delegates is
clearly the integers 0 to n - 1, each
taken once, but so also is the
collection of values of r, or else two
delegates would be correctly seated at    The eminent 16th century
the same time.  Summing the above         mathematician Cardan so
equations, one for each delegate, gives   detested Luther that he
S - S + nk, where k is an integer and S   altered Luther's birthdate
= n(n - 1)/2, the sum of the integers     to give him an unfavorable
from 0 to n - 1.  It follows that n = 2k  horoscope
+ 1, an odd number."  This contradicts
the original assumption.
    "I actually solved this problem
some years ago," Rybicki writes, "for a
different but completely equivalent
problem, a generalization of the non-
attacking 'eight queens' problem for a
cylindrical chessboard where diagonal
attack is restricted to diagonals
slanting in one direction only."