Alphonse, Bertha, Conrad, and Dagmar are sitting blindfolded in a room when hats are placed on their heads. They know that each hat is either red or blue. In fact, each person was given a red hat. Once the blindfolds are removed, each person can see what colour hats the other people are wearing, but can’t see his or her own hat.

(a) Suppose that it is announced that there is at least one person wearing a red hat. First Alphonse, then Bertha, then Conrad, and finally Dagmar are asked what colour hat he or she is wearing. Everyone can hear each answer. How should each person respond?

(b) Suppose, instead, that it is announced that there are at least two people wearing red hats. Do any of the responses in (a) change?