Puzzle Medley

Here are some of the other interesting puzzles we have discussed:
(Shane) Two real numbers are drawn from an unknown distribution. One of them is revealed to you. You now have to guess if the second is greater or less than the number revealed to you. Is there a strategy that is better than random guessing ?
(Ravishan) You have a line of length 1m with n marbles spaced out on it. Ravi then imparts a velocity and direction to each marble. What is the time until the last marble falls off the line ? Assume no friction and perfect collisions.
(muralib) You have 12 balls and a two sided measurement scale. One of the balls (unknown to you which one) is heavier or lighter than the rest. Can you use the balance three times and figure out which is the odd ball and whether it is heavier or lighter ?