Potpourri IV - Puzzling for Paralysis

In recognition of our 100th puzzle posted, we bring you "Potpourri IV". If you are new to the Grey Labyrinth, Potpourri Puzzles are a challenging collection of pandiscipline puzzles designed to test math, science, literature, logic, common sense, and trivia, with an occasional trick question thrown in. These problems are hard- it is unlikely that a single person can solve all twelve without assistance or a lot of research.

1. You have a ham sandwich with melted cheese on toast. With a single, perfect slice traveling along a two-dimensional plane, is it always possible to divide the sandwich so that the two halves have equal parts ham, cheese and toast? You may not assume an ideal sandwich- the ingredients may not necessarily be lying perfectly flat.
2. What's next in this series: 1, 26, 30, 42, 4...
3. An ant starts at one anchored end of a rubber band one meter long, and begins walking toward the other end at one centimeter per second. If the other end is pulled away at a rate of one meter per second, will the ant ever reach the end? Assume that the band is infinitely elastic, and that when pulled it stretches evenly across its length.
4. What was the original URL for the Grey Labyrinth in 1995?
5. In the late afternoon on December 3, 2000, in the North East skies over Bethlehem, a brilliant point of light lit up for a few seconds, far brighter than any planet or star had ever shined in those night skies. What was it? Be specific.
6. Which one of the following images does not belong? Image 1 Image 2 Image 3 Image 4
7. What is the mass of Earth's gravitational field?
8. A truncated icosahedron is an unusual polyhedron with 32 faces, 60 vertices, and 90 edges. Is it possible, starting at one vertex, to trace a path along the edges visiting each vertice exactly once, and then returning to the vertex where you started?
9. Young Jim Hawkins and five pirates had just recovered a chest of gold coins. Young Jim was entrusted to guard the gold while the pirates slept. During the night, one pirate awoke and divided the gold into five even piles, with one coin left over. He hid one pile for himself and gave the coin to Jim to keep quiet. Throughout the night the four remaining pirates did the same thing, each ending up with one left over coin which they gave to Jim. In the morning they discovered that the (now noticeably smaller) pile divided evenly into fifths. What is the fewest coins they could have began with?
10. How many different tastes can humans detect?
11. What is the fewest number of knights on a chess board so that every square is either occupied by, or under attack by, at least one knight?
12. Who, in a hurry, chose to go from Italy to India via Mongolia?

If you think you know the answers to all twelve questions, send them in! For Potpourri IV, in honor of our 100th puzzle, if someone submits all twelve correct answers before December 31, 2000, the Grey Labyrinth will donate $5000.00 to the Christopher Reeve Paralysis Foundation. Good luck, and happy puzzling!

---