Suppose there are 100 prisoners in a room. There are 100 different colors, and all colors are known to all the prisoners. Each prisoner gets a hat of a certain color. As usual, each prisoner can see everyone's hat except his own. The prisoners are asked to guess their respective hat colors simultaneously (they write their guesses on a piece of paper; their guess cannot … Continue reading the story "Prisoners and hats"
Monthly Archives for February, 2013
Imagine N cars, each of which travels at a different maximum speed. Initially, the cars are queued in random order at the starting point of a semi infinite, one lane highway. Each car drives at the minimum of its maximum speed and the speed at which the car in front of it is driving. The cars will form clumps. How many such clumps will we have in expectation? What is … Continue reading the story "Number of clumps of cars in a highway"