Edmund's Brainteasers
Problem 11
Solution
Problem 11: Another hats game. Solution
If Alice sees that all five people in front of her had red hats she knows hers is blue (since Jonathan only had 5 red hats). Hence not all those in front have red hats. Bethan knows this so if everyone in front of her has a red hat, knowing that not everyone in front of Alice has a red hat, she knows her hat is blue. But Bethan doesn't know - so not everyone in front of her wears a red hat. Continue the argument. The first person to see all red hats in front must be Edmund (since he is the first to know the colour of his hat). Edmund will then know that his hat is blue. The only person in front of him is Fiona who must therefore be wearing a red hat.