on our own

[azz]

Can one use
a. We were on our own.
instead of
b. We were each on our own.
?

Does this work
c. When it came to doing our homework, we were on our own. The supervisor did not help us. He just made sure that none of us helped anyone else.
?

Let us say, the kids are in a dormitory. They have a special time to do their homework. Each of them does their homework alone.

I think one has to include 'each' in (c) for it to make sense.

Many thanks.

[Phil White]

I think one has to include 'each' in (c) for it to make sense.

No, one has to make the context clear beforehand or reformulate the sentence in such a way that it is unambiguous.