Logic - The $1,000,000 Prize


Problem: You are selected as one of a team of ten individuals. The team is told that it has a chance to win a $1,000,000 prize. The team members are told that on the following day, the ten of them will be led into a room and arranged in a line (queue) so that each person can see only those in front of him. Each person will then be blindfolded and a hat will be placed on each individual's head. Some of the hats will be red while others will be green, but no one knows how many are red and how many are green. Once all the hats are in place, the blindfolds will be removed. No one can see the color of the hat on his own head nor on the head of anyone behind him, but will be able to see the color of the hats on all of those in front of him in the queue. Each member of the team, starting with the last in the queue and proceeding forward, will then be asked the question, "What color is the hat on your head?", to which the individual must respond with a simple "red" or "green" – no tricks. The response given by each individual to this question will be able to be heard by all other members of the team. The team needs to devise a scheme so at least nine of the ten will be able to answer this question correctly. If at least nine of the team members do answer the question correctly then the team wins the $1,000,000 prize which is to be divided evenly among the ten, otherwise no prize is given. Can you devise a scheme along with your team members so that your team will be guaranteed to win the million dollars?