What is the shortest distance to get from one corner of a unit cube to the extreme opposite corner, without leaving the surface of the cube?

The chance of winning the lottery is 1 in 100 million. Ifyou stacked all 100 million lottery tickets on top of another, how high would this stack be, in meters? Is the answer closest to:a)     Distance from New York to Boston?b)     Diameter of the earth?c)     Height of a 20-story apartment?d)     Length of Manhattan (north-south) at the longest stretch?e)     Height of Empire State Building?

You roll a die until a number other than 1 appears. You get the same number of dollars as there are dots on the upturned face of the die. What’s the expected payoff to the game?

You have 10 coin slots, each capable of giving you at most 10 pennies. However, you know that one of the coin slots is defective, and gives you fake pennies that are lighter than the normal pennies by 0.1 gram. Suppose you have a digital balance and know the mass of a normal penny. Using the balance only once, how can you determine which of the coin slot gives you fake pennies?