Edmund's Brainteasers
Problem 4
Solution
Problem 4: The five hats. Solution
Marie-Louise argued as follows. Suppose my hat is blue. Then David will see one blue hat and one black hat. But in this case David knows that if his hat were blue then Gavin, seeing two blue hats would know at once that his was black (there are only two blue hats). He has not instantly claimed the prize so then David would know his hat is black and he would claim the prize. But David has not claimed the prize after a few moments, so Marie-Louise knows her hat is not blue. Then it must be black.