



Potpourri IV  Puzzling for Paralysis
by Kevin J. Lin
As promised, the Grey Labyrinth donated $5000.00 to the Christopher
Reeve Paralysis Foundation. Below are the "official" solutions
to the twelve potpourri questions. You can read about how these were deduced
in the Discussion
Forums.
 Yes. In fact there's a mathematical theorem which literally states
this. It's called the Ham
Sandwich Theorem (no, really).
 The next number is 29. This isn't a mathematical series, they're the
first few room numbers of the correct solution to Christopher Manson's
famous puzzle book, "Maze".
 Yes. See the Discussion
Forums for a detailed explanation.
 The answer we were looking for was http://www.cybercom.net/~kevinlin/labyrinth.
However, some pointed out that a previous post mentioned that the Grey
Labyrinth didn't officially exist until 1996.
 This was the question that gave people the most difficulty. For one
thing, by coincidence there were two (incorrect) answers that seemed
highly plausible. One, the ISS opened its solar collectors on that day
bright, but doubtfully brighter than Venus gets. Two, rockets were fired
in part of the ongoing IsraeliPalestinian conflict. Possibly a correct
answer, but how would we have known that rockets were going to be fired
that day? The answer we were looking for was an Iridium Flare, specifically
Iridium 16 which reached 8 magnitude. If you don't know what an Iridium
Flare is, or have never seen one, I strongly suggest visiting the Satellite
Visibility home page and finding out when you can see one where
you live. On a clear night outside the city, Iridium Flares are spectacularly
bright.
 Image 4 does not belong. All the images have something in common
they represent answers to Potpourri Puzzles. But the first three all
represent answers Potpourri Puzzles numbered 6. The fourth image represents
"Maze" which was the (at time of posting) unsolved puzzle
#2.
 3 trillion tons. The Earth's gravitational field has energy, which
according to relativity, has mass. You read about it at Scientific
American or at the home page of Gravity
Probe B (see the Relativity Q&A section).
 Yes. This type of problem is known as a Hamiltonian Circuit, after
the mathematician William Hamilton. Hamilton tried (unsuccessfully)
to market a game based on solving these circuits for a dodecahedron.
Determining if an arbitrary graph has a Hamiltonian Circuit solution
is an NPcomplete problem; i.e., there is no generalized solution that
is significantly faster than "brute force". Borschevsky came
up with a graph in the Discussion
Forums. Coincidentally, after I posted this puzzle I received an
email from my father. Apparently one of my cousins studies Hamiltonian
Circuits and the related "Traveling Salesman Problem", and
sent my father a program he wrote that graphs these solutions.
 3121. See the Discussion Forums for details.
 Five. Although humans can detect tens of thousands of distinct flavors,
these are composites of five basic tastes plus a much larger number
of scents. If you had no sense of smell, all foods would only be comprised
of five tastes: sweet, salt, bitter, sour, and umami.
The fact that umami had its own taste buds was only recently discovered.
The umami taste is most strongly associated with monosodium glutamate
(MSG).
 Twelve. Coyote made a lovely graphic of this in the Discussion
Forums.
 Phileas Fogg, the protagonist of Jules Verne's Around the World
in 80 Days went from Italy to India via the steamer "Mongolia".
I hope everyone enjoyed the Grey Labyrinth's 100th puzzle. Much thanks
to everyone who worked on it.

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