Question: Five pirates are parting ways after finding a treasure of 100 pieces of gold. The pirates decide to split it based on a vote. Each pirate, from oldest to youngest, gets to propose a plan on how to split the gold.
If at least 50 percent of the other remaining pirates agree on the plan, that is how they will split the gold. If less than 50 percent of the pirates agree, the pirate who came up with the plan will be thrown overboard. Each pirate is smart, greedy, and wants to throw as many others overboard as possible without reducing the amount of gold they get.
What plan can the first (oldest) pirate propose to live and get as much gold as possible?
Answer: He can propose a plan that he gets 98 pieces of gold, the 3rd pirate gets 1 piece, and the 5th pirate gets 1 as well.
If there were just 2 pirates the younger pirate would definitely deny the plan so he could get all of the gold.
If there were 3 pirates the first pirate can offer the second pirate 1 piece of gold and take the rest himself because the second pirate wouldn't get anything if he has to propose a plan himself.
If there were 4 pirates the first pirate could take 99 for himself and offer 1 to the youngest pirate. They would both agree. If the youngest disagrees then he won't get any gold in the next plan.
So when there are 5 pirates it is in the interest of the 3rd and 5th pirate to accept 1 piece, because if they don't they won't get anything in the next plan.
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.