Is there a single word that means "each of which"?

Question

I usually use each of which like as follows:

One big problem is decomposed into a number of subproblems, each of which implies that blah blah blah.

---

One day, I came across a word in a book that perfectly matched each of which. I memorized the word at that time, but now I forgot :-(

If anyone knows this word, please let me know. I'm not sure but I remember that it was a single word that composed of relative pronoun and preposition, like whichamongof.

Answer 1

With some very slight changes: each

One big problem is decomposed into a number of subproblems, each implying...

Or

One big problem is decomposed into a number of subproblems; each implies...

Answer 2

There is the relative pronoun whereof (archaic) but it does not include each in its meaning. Whereof means:

of which or what:

• He sees hostility, the cause whereof he does not know. (Cambridge)

Your sentence could be re-written as:

One big problem is decomposed into a number of subproblems, whereof each implies that ...

There is also whereamong, but it is even more uncommon than whereof.