Just think of a number between 1-1,000,000 the cat is guaranteed to guess it using the best method possible!
This project works, because every time you answer your eliminating half the candidate pool, and Log_2(1,000,000)~19.93 Based on my tests, it is not possible for the cat to guess incorrectly, you would've done something wrong. Please keep in mind there's a greater then 50% he guesses your number before guess #20. I'm embarrassed that it took me like 20 minutes to realize there's a "round" button.
