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.
The theorem to be proved is that if any even number of people
take seats at random around a circular table bearing place cards
with their names, it is always possible to rotate the table until
at least two people are opposite their cards. Assume the contrary.
Let N be the even number of persons, and let their names be replaced
by the integers 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 same time. Summing
the above equations, one for each delegate, gives S-S+NK, where
K is an integer and S=N(N-1)/2, the sum of the integers from 0
to N-1. It follows that N=2K+1, an odd number." This contradicts
the original assumption.
Look for this snowflake - it has magic properties