Algernon, Balthazar and Caractacus are standing together. Their friend, Daniel, shows them an open box that contains 3 red and 2 green hats. There’s nothing else in the box. All the 3 are then asked to close their eyes, take a hat from the box and put it on their head.
Daniel closes the box and asks them to open their eyes. Now, each of them can see the colour of the hat worn by the other two. They, however, do not know the colour of their own hat, nor which hats are left in the box.
Algernon says: ‘I don’t know the colour of my hat.’
Balthazar then says: ‘I don’t know the colour of my hat either.’
Finally, Caractacus says: ‘I know the colour of my hat!’ What colour is it?
Note: Each person can hear what the other 2 are saying.
Difficulty rating:
Easy. 4/10
Solution:
If Algernon would have been seeing 2 green hats then he would have surely known his own hat color. In all the other cases, he won't be able to know his hat color. So, after he says, "I don't know" , B and C know that the 2 hats on their heads are not both green.
After hearing Algernon, B knows that either
Scenario 1: he and C both have red hats, or
Scenario 2: one of them has a red hat on and the other has a green hat.
If B would be seeing a green hat on C then he would immediately know that his hat is red. But, if he were to see a red hat on C, then he won't know if they are in scenario 1 or in scenario 2 and would end up saying, "I don't know".
And this is exactly what happens. B says, "I don't know" and this tells C that C is not wearing a green hat. Thus, C knows that he has a red hat on and says so.