Pico Fermi Bagel

A guessing game where the answers tell you how close you are, but never where.

I am thinking of a number made of three different digits. You guess a number, and I reply with one word for each digit you got something right about:

Fermi

A digit that is right, in the right place.

Pico

A digit that is in the number, but somewhere else.

Bagels

Nothing. None of those digits are in it at all.

What makes it hard is that I never say which digit earned which word. Two Fermi and a Pico tells you a great deal about how close you are and nothing whatsoever about where to look — you have to get that by comparing one guess against the next.

The digits are always different from each other, and a leading zero is allowed, so 047 is a perfectly good three-digit answer.