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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."

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