Question: A prison has 23 prisoners in 23 different cells. The prisoners have no way to communicate with each other in any way from their cells. There is another room, the rec room, that has two switches on the wall (A and B). The switches have on and off positions but they start in an unknown position.
Prisoners are randomly taken to and from the rec room one at a time. They must change the position of only one of the two switches each time they go to the room. At any point a prisoner can yell out, "Every prisoner has been here!" If the prisoner is correct that all of the prisoners have visited the rec room, then they all go free. If they aren't correct then they are all executed.
Before they start they are given one planning session during which they can discuss a method to win the game. What method can they use to ensure they all go free?
Answer: Here are the rules they can use to ensure they will all go free eventually:
The prisoners will choose one 'leader' and everybody else will be a follower. If you are a follower:
Question: There is a 100 pound watermelon laying out in the sun. 99 percent of the watermelon's weight is water. After laying out for a few hours 98 percent of the watermelon's weight is water.
How much water evaporated?
Answer: 50 pounds.
In the beginning it is 99 pounds water and 1 pound other stuff. At the end the 1 pound other stuff is 2 percent so the total weight is 50 pounds. 50 pounds - 1 pound other stuff = 49 pounds water. So 99 pounds - 49 pounds = 50 pounds water lost.
Question: You find me behind the stars; or in a sixth, seventh, or third.
It takes something round, a computer, and me to make pie.
I am bigger than anything you can think of.
What am I?
Answer: Infinity (A sixth, seventh and third all go on forever in decimal form. Pi instead of pie).
Question: Thomas has missed an excessive number of days of school, so he must meet with Principal Davis. Mr. Davis asks him "Why on Earth have you missed so many days?"
Thomas replies "There just isn't enough time for school. I need 8 hours of sleep a day, which adds up to about 122 days a year. Weekends off is 104 days a year. Summer vacation is about 60 days. If I spend about an hour on each meal, that's 3 hours a day or 45 days a year. I need at least 2 hours of exercise and relaxation time each day to stay physically and mentally fit, adding another 30 days.
Add all of that up and you get about 361 days. That only leaves 4 days for school."
The principal knows Thomas is full of it, but can't figure out why. Where is Thomas going wrong?
Answer: There are two reasons:
First, Thomas is double counting a lot of the days. A lot of the time spent sleeping, eating, and relaxing occurs during weekends and the summer. Weekends also occur during the summer, so all of these hours are getting counted several times.
Secondly, school isn't an all day thing. So the 4 days actually represents more days of school. If school is 6 hours per day, those four days represents 16 days of school.
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