The problem is threefold?

The problems are threefold.
The problem is threefold.

Which is the right way to use the -fold suffix?

Note - This question was previously asked by a user whose account has been suspended, so the question was auto-deleted. I'm re-posting now it because I think this is a valid question.

Solution 1:

The actual question does not seem to quite compare like with like due to pluralization, e.g.

The problems are threefold.
Could seem to - possibly - mean multiple problems have 3 parts to each of them.

The problem is threefold.
One problem has three parts. Definitely just One problem (but with 3 parts).

The is and are are getting used based on the pluralization of problem, after all one can't have "problem are" or "problems is".

In practice both forms are basically usually used to mean the same thing, 3 parts to one thing.

Solution 2:

If I heard someone speak your first sentence, I would assume that there is a set of problems, and that each problem in that set is threefold. If I heard the second, I would assume that there is a single problem, and that this problem is threefold.