Three students enter a room, and a white or black hat is placed on each of their heads.
(The colour of each is determined by a fair coin toss, thus each person is equally likely to have a black or a white hat, independent of the other students).
Each student can see the other students’ hats, but not his/her own. No communication of any sort is allowed, except for an initial strategy session before they enter the classroom.
Once they have had a chance to look at the other hats, the students must simultaneously guess the colour of their own hats or ‘pass’.
The students share a prize of £3 million if at least one guesses correctly and none of them guesses incorrectly.
What should their strategy be?
(Hint: If one person only speaks, and says white, they win 50% of the time. But this is not the optimal strategy! What is?)
