(i) Their father puts a hat on each of their heads and says: “Each of your hats is either red or blue. At least one of you has a red hat.” Alice then says “I know the colour of my hat.” What colour is each person’s hat?
(ii) Their father puts a new hat on each of their heads and again says: “Each of your hats is either red or blue. At least one of you has a red hat.” Alice then says “I don’t know the colour of my hat.” Bob then says “I don’t know the colour of my hat.” What colour is Charlie’s hat?
(iii) Their father puts a new hat on each of their heads and says: “Each of your hats is either red or blue. At least one of you has a red hat, and at least one of you has a blue hat.” Alice says “I know the colour of my hat.” Bob then says “Mine is red.” What colour is each person’s hat?
(iv) Their father puts a new hat on each of their heads and says: “Each of your hats is either red or blue. At least one of you has a red hat, and at least one of you has a blue hat.” Alice then says “I don’t know the colour of my hat.” Bob then says “My hat is red”. What colour is Charlie’s hat?
(v) Their father puts a new hat on each of their heads and says: “Each of your hats is either red or blue. Two of you who are seated adjacently both have red hats.” Alice then says “I don’t know the colour of my hat.” What colour is Charlie’s hat?