Game of BAGELS

I’ll think of three digits (0 .. 9), no two the same. You try to deduce what those digits are, and what order they are in, by entering three digits of your own (no two the same). I’ll give you clues about how your digits compare with mine. On the basis of those clues, you enter three more digits, get more clues, and so on.

• “Bagels” means that none of your digits match any of mine.
• “Pico” means that one of your digits (but I won’t tell you which one) matches one of mine, but is not in the same position as mine.
• “Fermi” means that one of your digits (but I won’t tell you which one) matches one of mine and is in the same position as mine.

For example, if my secret number is “068” and you enter “678”, I’ll respond “Fermi Pico” — “Fermi” because you entered an ‘8’ and I have ‘8’ in the same position as yours; and “Pico” because you entered a ‘6’ and I have a ‘6’ but not in the first position as yours is. (The ‘7’ in your guess is not one of my digits, but I’ll remain silent about that.)

Another example: If my number is “068” and you enter “687”, you’ll receive “Pico Pico”.

The game is won when you receive “Fermi Fermi Fermi”.