Our 2n hat wearing friends are once again standing in a circle so that everyone
can see everybody else’s hat. At a certain moment in time each person must
simultaneously shout “my hat is black” or “my hat is white”. The team wins a
big prize if at least n of the people get the color of their hat right. Of course, if
fewer than n get it right, the whole team is eliminated and this is painful. Can
they guarantee to avoid being eliminated?
