19.7. Three wise men are sitting on chairs back to back, so the one sitting in front cannot see those sitting behind. They know there are 3 white and 2 black hats. The wise men close their eyes and hats are placed on their heads, after which the remaining hats are removed. The wise men open their eyes, and the one sitting at the back says that he does not know what color hat he is wearing. After this, the one sitting in the middle says that he also does not know what color hat he is wearing. Does the one sitting in front now know what color hat he is wearing?
19.7. Answer: the one sitting in front knows that he has a white hat. If the two sages in front had black hats, then the sage sitting at the back would know that he has a white hat. Therefore, at least one of them has a white hat. So, if the sage sitting in front had a black hat, the one sitting in the middle would realize that he himself has a white hat. Therefore, the sage sitting in front has a white hat.