Will searching my dusty bones only give me pieces I don't have?

I've been collecting piles of dusty animal bones in hopes of getting all the pieces for the misshapen animal skeleton.

So far it doesn't seem like I've gotten doubles of any of the pieces, which makes me hope that I will always get bits I don't have, if I get anything out of the piles.

Is this true? If they drop anything, will the drops always be bits I don't already have?

Unfortunately no, you will get dupes. You may not have gotten dupes yet because there are a lot of different bones that can possibly drop. But as you get more individual pieces, the chances of a new piece being a dupe of one you already have increases too.

What you may want to do as you get close to getting all the bones is to buy the specific pieces you are missing from the mall instead of opening tons of piles hoping you get the specific piece you need. There is probably some math to figure out the exact optimal time to do this, but I'm not up to calculating it. I would probably just buy the specific bones once you open up around 10 piles in a row and all of the bones you get are dupes.

For the math inclined, here is Riff, a KoL Dev, asking for math help on how many piles of bones are needed to have a specific probability of getting all the specific bones

Piles = 3.7 * log(1 - Prob^.01) / log .99

where Prob is the threshold you set (.5 or .99)