Potpourri IV - Puzzling for Paralysis

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.

1. Yes. In fact there's a mathematical theorem which literally states this. It's called the Ham Sandwich Theorem (no, really).
2. 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".
3. Yes. See the Discussion Forums for a detailed explanation.
4. 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.
5. 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 Israeli-Palestinian 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.
6. 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.
7. -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).
8. 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 NP-complete 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.
9. 3121. See the Discussion Forums for details.
10. 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).
11. Twelve. Coyote made a lovely graphic of this in the Discussion Forums.
12. Phileas Fogg, the protagonist of Jules Verne's Around the World in 80 Days went from Italy to India via the steamer "Mongolia".