Is my hat black or white?
Guess the color of your own hat by looking at the hats on the others.
There are N = 2n-1 people who are offered a challenge. If they win, they each get a million dollars. The men are blindfolded, and white or black hats chosen randomly are placed on their heads. The blindfolds are removed so they can each see the color of the hats on the other N-1. They must either guess the color of the hat on their heads or pass. If all pass, they lose. If one gets it wrong, they lose. If the answers are either pass or correct, with at least one correct, they win. What is the probability they will win a million dollars each? (Problem and Solution from Rutgers mathematics Professor Siddhartha Sahi, one of the original founders of our science club in Princeton and a colleague and friend of Gyan’s). The solution can be found here.