logic
posted by unowen .
Ali and Zoe reach into a bag that they know contains nine lottery balls numbered 19. They each take one ball out to keep and they look at it secretly. Then, they make the following statements, in order:
Ali: "I don't know whose number is bigger."
Zoe: "I don't know whose number is bigger either."
Ali: "I still don't know whose number is bigger."
Zoe: "Now I know that my number is bigger!"
Assuming Ali and Zoe are perfectly logical, what is Zoe's smallest possible number?

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