Edmund's Brainteasers
Problem 11
Problem 11: Another hats game
The game Marie-Louise, David and Gavin played at the All Saints' Annual Party (Problem 4) proved so popular that Jonathan devised a new hats game for the following year. This new game involved six players: Alice, Bethan, Charles, David, Edmund and Fiona. Jonathan has 5 red hats and 6 blue hats. The six players sit in order one behind the other with Alice at the back and Fiona at the front. Jonathan puts a hat on each player so each can see the hats of those in front, but not, of course, their own hat or the hats on the people behind. Jonathan asks each in turn, beginning with Alice, if they can tell the colour of their hat. Alice doesn't know, nor does Bethan, nor Charles, nor David. However when Jonathan asks Edmund he replies that he knows the colour of his hat. What is the colour of Edmund's hat? What is the colour of Fiona's hat?