It’s been a while since the first challenge which was a cipher. This challenge is about finding numbers through combinational reasoning. It is not very difficult but it requires some thinking. If you find the answer, post it in the comments. Don’t worry, I will never show the answer. I will edit the comment before approval and I will let you know if you were right or wrong.
A wise man whispers a number to each of his three apprentices, Alice, Bob and Carol. All numbers are integers larger than zero. Wise man tells to them that the sum of their numbers is 14 and ask them in order if they know all three numbers. Alice responds that she does not know the numbers but she knows that Bob and Carol have different numbers. Bob responds that he does not know but, even before hearing Alice response, he knew that all of them have different number. After hearing both responses, Carol says that she knows all three numbers. Which numbers have the three apprentices?