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please help me figure out how to do this

I wont lie, this is for a homework problem and I have searched on google for a long time and still can't figure out what to do.

here is the problem

So there's a folder let's say called "bare"
in it, there are 10 dirs with names from "part1" through "part10"

in each part dir
there are many txt files most beginning with a number but some beginning with spm

those beginning with spm are spams and I need to figure out how many spams there are

to find the total number is easy

find . -name 'spm*' | wc

however the next part is hard

somehow I have to find a way to find out how many spam files there are in each part1-part10 dir.

And I can only use one compound command to do it.

I thought about

find . -name 'part*' -exec find . -name 'spm*' | wc

or find . -name 'part*' -exec find -name 'spm*' | wc

or whatever variations of this

all return find incomplete

please someone help

thank you very much

prof provided this hint which I dont really understand but may be of help

the GNU version. In particular, the printf option is very helpful. Google will lead you to some helpful tutorials on find (the GNU verison). To use the GNU version, it is similar to the posting about using grep. In other words, you must either call the GNU version using
/usr/local/GNU/bin/find
or ssh into treebeard.berkeley.edu and use the find command there.

Thread closed due to homework rule violation.