# Re: Eight geographical points

On Feb 25, 7:03 am, James Dow Allen <gm...@xxxxxxxxxxxxxxxxxxxx>
wrote:
jonnie303 <john.gri...@xxxxxxxxxxxxxx> might have writ, innews:a63d6ed7-3fe6-420d-9703-270feb442261@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:

On Feb 23, 3:50 pm, James Dow Allen <gm...@xxxxxxxxxxxxxxxxxxxx>
wrote:
I constructed a list of eight places on Earth; the list has a certain
property.
To make the problem harder, I've omitted two items from the list;
each of the omitted places is an inhabited settlement.

(1) What are the two inhabited places I've omitted?
(2) What property does the list possess?
(3) Can you a find a different list of eight inhabited places with
the same property?

A. Arroyo la Vaca, SW of Cuidad Acuna, Coahuila, Mexico.
C. Matinhos, sea-side town near Curitiba, Paran, Brazil.
D. Maxixe, largest city in Inhambane Province, Mozambique.
E. ___________ ???
F. Pandaan, 25 miles south of Surabaya, East Java, Indonesia.
G. ___________ ???
H. Tyumsyu 400 miles ENE Of Yakutsk

What an interesting puzzle. After plotting the points on Google Maps,
without achieving enlightenment, the breakthrough came when I got out
my old globe and marked the places with pieces of sticky paper. It
certainly challenged my misconceptions about the relative positioning

I also found the relative positionings, when plotted, quite surprising.

of the points. I've come to the conclusion that the answer to (2) must
be that each of the eight places in the list is equidistant from 4 of
the others, thanks to the miracles of spherical geometry. And I'm
prepared to take a stab at question (1), if only to prevent myself
spending even longer on the problem - my tentative guesses are Scott
Base, Antarctica, and Baker Island in the Pacific Ocean. I'll leave
question (3) for another day.

Good!  But Baker Island is neither inhabited (according to Wikipedia) nor
does it satisfy the criteria quite as closely as the other seven places
on the list.  I'll consider it correct, however, if only to prevent you
from spending even longer on the problem!  :-)

Really nifty, IMHO, is that three consecutive points on the list are in
Portuguese-speaking countries, but this was a "red herring."

The intended question (2) to which these eight points are an answer is
"Find eight (inhabited) points on the Earth's surface which ________
the ______ pairwise _______."

Obpuzzle:  Prove or disprove whether all lists of 8 points such that any
is equidistant to 4 of the others satisfy the intended criterion.

James Dow Allen- Hide quoted text -

- Show quoted text -

must have been to construct in the first place. What mapping/distance
tools did you use? And more fundamentally, how did you determine the
common distance which underlies the puzzle?

-----------------
jonnie303
sevenoaks, uk
.

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