You travel 100 km north, 100 km east, and then 100 km south. You are at the same point that you started from. Where are you?

There are 3 cards: one is all red, one is all blue, and the third is blue on one side and red on the other. The cards are shuffled. You pick one at random and it is blue on the side facing you. What is the probability that it is also blue on the other side?

In a far away land, there is an unusual tribe of 300 perfectly logical and perfectly intelligent people. Each member has a visible spot on the back of his or her head, some are red and some are black. Nobody knows the color of their own spot, but they do know the color of everyone else's. If a tribesman ever realizes the color of his own spot it is strict custom that he publicly commits suicide the following morning, so they never mention spot colors, and have no mirrors. But then one day an American tourist visits this land and announces to the entire tribe: "I can see that at least one of you has a red spot." The tourist leaves and returns a year later. What has happened?

You are shipwrecked on an island. There is a fork in the path to the other side, one way leads to a safe village, the other leads to hungry cannibals. There are twin brothers who both know which path is which, but one of the brothers is honest, and the other always lies. You may ask one of them a single question. What should it be? What question would you ask if there is just one person who is honest or lies but you don't know which?