The great town wizard needs a new apprentice, and has announced a competition for the post. Many applicants have tried, and only the three brightest remain for the final challenge.
The wizard gives each applicant a hat, and tells them that they have either a black or a white hat. The first one to figure out the color of her own hat and publicly announce it wins the challenge, and becomes the wizard's apprentice. Also, if any of them sees another applicant having a white hat, they are supposed to say:
"I see someone with a white hat."
However, the wizard, devious as she is, has given white hats to all three applicants. So, predictably, they all immediately announce that they see someone with a white hat, and then nothing happens for a while.
But, after a few minutes of silence, the most clever of the applicants announces: I have a white hat! She becomes the wizard's apprentice, and everyone lives happily ever after.
How can she know the color of her hat?