The Third Sage Speaks

Three sages are shown a collection of five hats: three are white and two are black. While their eyes are closed, each sage is given one hat to wear. The two unused hats are hidden. Once they open their eyes, each sage can see the hats worn by the other two, but not their own. They all know exactly how many hats of each colour were available. The first sage is asked whether he can determine the colour of his hat. He says, “No.” The second sage hears this answer, studies the other two hats, and is asked the same question. He also says, “No.” The third sage then announces that these two answers have allowed him to determine his own hat colour. What colour is the third sage’s hat?