I have a clock in my house, on the wall.
On a summer's day I forgot to wind it and it stopped. Then I went to visit a friend who had a watch that was always right on time. After I stayed for a bit, I went home, made a simple alteration and set the clock just right.
Now how did I do this when I had no watch on me to tell how long it took me to come back from my friend's place?
Before I left, I wound the wall clock. Upon my return, the amount of change that I could see in the clock is how long it took to go to my friends place and come back, adding to that the time I spent there, which I know because the clock at my friend's place is accurate.
Subtracting the time of the visit from the time I was absent from my house, and dividing by 2, I obtained the time it took me to return home. I added this time to what my friend watch showed when I left, and set the sum on my wall clock.
Two sentries were on duty outside a barracks. One faced up the road to watch for anyone approaching from the North. The other looked down the road to see if anyone approached from the South. Suddenly one of them said to the other, "Why are you smiling?" How did he know that his companion was smiling?
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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