April 22, 2015
Problem of the Week
for Tuesday April 22, 2015
In the second episode of the second season of the quiz show called "Hats", a black, white, or red hat is placed on the three teammates' heads, and the team wins the competition if the one person on the team who volunteers to make a guess is able to correctly determine the color of the hat that he wears. The producer of the show guarantees that at least one of the hats placed on the three heads will be red. Each will see the hat on the other two players' heads but not the one on his own.They have no way of communicating or sending signals to each other once the hats are placed other than by not volunteering to make a guess. If they are allowed to meet beforehand to work out a strategy, what plan will guarantee a victory? Note that if at the end of round one, no one volunteers to make a guess, the team will be allowed a second round for someone to volunteer, and if at the end of the second round, still no one volunteers, the team will be allowed a third and final round for someone to volunteer and make a guess.