There are three genii standing in a row in a room facing the same direction. Thus, the genius at one end can see the two genii ahead of him, the genius in the middle can only see the one genius ahead of him and the genius at the front cannot see anybody.
You tell the genii that you have 5 hats: 3 red hats, and 2 white hats. You then blindfold them, randomly place three of the hats on their heads and hide the remaining hats. You remove their blindfolds and ask them to say the colour of their hats.
The genius at the back says “I don’t know what colour my hat is.” The genius in the middle says “I don’t know what colour my hat is.” The genius at the front says “My hat is ______.”
Fill in the blank.
Since the genius at the back does not know what colour his hat is, one or both of the front two genii must be wearing a red hat.
Since the middle genius does not know what colour his hat is, the front genius cannot be wearing a white hat.
Thus, the front genius must be wearing a red hat.