Required Mathematical Intelligence

Chapter 18 The Hat Problem ([-])

The teacher called his three most proud students together and wanted to test their intelligence.He first asked the three students to stand in a row, and then took out five hats, three white and two black, and asked the students to hide the two black hats after seeing them, and gave them three white hats to wear.None of the three students could see the hat they were wearing, but the one in the back could see the one in the front, and the one in the front couldn't see the one in the back.The teacher asks three students to name the colors of the hats they are wearing.After thinking for a while, the student in front replied: I am wearing white.How did he know?
[Answer: He analyzed it like this: If I and the second person wear black hats, the people behind will know the color of their hats immediately, but he didn't answer, which means that at least one of the second person and I wears a white hat .If I was wearing a black hat, since the third person didn't answer, the second person could quickly deduce that he was wearing a white hat, but he didn't answer either, which meant that I was not wearing a black hat. ]
(End of this chapter)