Three people, named Adam, Beth, and Carl, are standing in a straight line, facing forward. Carl can see both Adam and Beth, Beth can see only Adam, and Adam cannot see anyone.
There’s a pile of 5 hats in a cupboard – three blue hats and two red hats. Adam, Beth and Carl are each given either a red or blue hat from the cupboard without being able to see which they’ve been given.
They know there were three blue hats and two red hats, but they don’t know which colour they are wearing.
Carl is asked whether he knows the colour of his own hat. Carl answers, “No, I don’t know.”
Beth, who can see only Adam, is asked the same question. She also replies, “No, I don’t know.”
Finally, Adam, who cannot see anyone, is asked the same question.
He confidently answers, “Yes, I know the colour of my hat.”
What colour is Adam’s hat, and how can he be so sure?
Adam can confidently determine the colour of his hat based on the responses from Carl and Beth.
When Carl sees Adam and Beth, he has two possibilities:
- Both hats are the same colour (either both red or both blue).
- Their hats are different colours (one red and one blue).
Carl said he didn’t know. If Carl saw red hats, he could have deduced that his hat must be blue. So Adam and Beth cannot both be wearing red hats.
So Adam and Beth must be either both in blue hats or one must be wearing a red hat and the other a blue hat.
Now, Beth knows that Carl sees either one red and one blue hat or sees two blue hats. If Beth sees a red hat on Adam, she would deduce that her hat is blue, as Carl would have known his hat colour if he saw two red hats.
Because Beth doesn’t know what hat she is wearing, she cannot have seen a red hat on Adam.
Therefore, Adam knows that his hat must be blue.
