Using a pool of problems, 16 tests will be formed.

-Every test should have the same number of problems.
-Any problem should be included in at most 8 tests.
-For every 4 tests, there should be at least 1 problem common to all of them.
-Within a test a single problem cannot be used more than once.
-Some tests may be formed of exactly the same problems.

What can be the minimum number of problems in this pool?

If the problem was asked for 8 tests, any problem to be included in at most 4 tests and at least 1 problem common to every 2 tests then the answer would be 6: