Dr. Miller was staying with his cousin, Alfred, in Alfred’s lakeside cabin. They were setting up Alfred’s will. Since Dr. Miller was Alfred’s closest living relative, much of Alfred’s estate was being left to him.
One day, Alfred went to Dr. Miller very upset.
“Doctor,” he began, “I have just found out that an old enemy is out to get me. He is coming very soon. Where will I go? Where can I hide? If he finds me, he will surely kill me. I do not have time to leave this cabin and hide in the woods.”
Dr. Miller thought for a moment, and then grabbed a 5′ long bamboo fishing pole, with a diameter the size of a quarter.
“Alfred, follow me out to the lake. This lake is 4′ deep. If you lie on the bottom of the lake and breathe through this pole, your enemy will never find you. I will be in the bulrushes with a shotgun, and I will shoot him when he comes. I will swim down to find you when he is gone.”
Alfred thought that was a great idea and went down to the lake with the bamboo pole in his mouth.
A few hours later, a ranger passed by. He found Alfred’s body. Dr. Miller told the police of the circumstance, and that Alfred had probably panicked, and died.
Police arrested Dr. Miller on the charge of murdering Alfred. Why?
The pole was 5′ long, but only the size of a quarter. The first time he breathed in, he breathed oxygen. When he exhaled, the air could not travel 5′ before he breathed in again. He was just breathing what he exhaled. Before long, all he was breathing was carbon dioxide. He died of CO2 poisoning. Dr. Miller was the one who told him to use the pole. However, he was knowledgeable about the human body and knew breathing only carbon dioxide would result in Alfred’s death. His motive? The money in Alfred’s will.
5 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?
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.
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