I love the puzzle below because it doesn’t seem like there’s enough there to answer it. The secret lies in imagining yourself in the head of each princess as they imagine themselves in the head of their sisters. It requires a fantastic leap of imagination. I’m not going to solve it for you, but consider:
- What does the eldest sister know about her sisters’ hats?
- What does the middle sister know from the fact that the eldest sister doesn’t know her own hat?
- What does it tell us that even with this information she doesn’t know the color of her own hat?
Three princesses are taken prisoner by an ogre. For sport, the ogre puts them in a row from eldest to youngest, so that each sister can only see her younger sisters. Then he blindfolds them and says, “I have three white hats and two black hats. I will put one hat on each of your head. If any one of you can tell me the color of your own hat when I take off your blindfold, I’ll let all three of you go.”
The ogre takes the blindfold off the eldest princess. She looks ahead at the hats on her two younger sisters, thinks, and finally says, “I don’t know what color my hat is.”
The ogre takes the blindfold off the middle princess. She looks ahead at the hat on her younger sister, thinks, and says, “I don’t know what color my hat is.”
Then the ogre takes the blindfold off the youngest princess. She looks ahead into the woods–she can’t see anyone else’s hat. Then she thinks, and says, “I know what color my hat is.”
What color is her hat and how did she know?