Question: You come to a cross road and see a man with two heads. A sign tells you that one head always tells the truth and the other one always lies. The sign also tells you that one road leads to life and posterity while the other leads to certain death. Now the hard part. You can only ask ONE head ONE question. What do you ask? Which road do you take? Hint: One head knows what the other will tell you.
Answer: You ask, "Which road would the other head say." You then take the opposite road. Explanation. If you happened to ask the truth teller he would tell you that the liar would say the wrong road. Therefore you would take the opposite road. If you happened to ask the liar which one the truth teller would say he would lie and say the wrong road. You then would take the opposite road.
Question: Your father is a scientist who has invented a red pill which, if eaten with 1 blue pill which he has invented, will grant immortality. The night he invents it, he gives you 2 red and 2 blue pills just in case one of them is lost or substandard. He also warns you that an overdose will cause the opposite effect and kill you instead. You put the pills in your pocket and leave his lab for home. On the way home, you are abducted by aliens who blindfold you and throw you into a singularity. At this point, you remember the pills your father gave you. You take them out (you can move and have enough oxygen in space for a short time), but realize that you can't tell the red pill from the blue pill. Even if you take off your blindfold, you can't see anything due to your proximity to the black hole. Given the circumstances, how do you successfully eat 1 red and 1 blue pill and survive?
Answer: Eat half of each pill.