100 Day Summer Challenge

100 problems in 100 days. #100problems

Day 73

73 of 100: I Know What You're Thinking But Do You Know What I'm Thinking?

Logic Level 2

Ali and Zoe reach into a bag that they know contains nine lottery balls numbered 1-9. 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?

Hint: When she speaks for the first time, if Ali doesn't know whose number is bigger, which number must she not have?

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