The output of the tests is not very informative in Clojure. Use the are macro, like this:

(deftest tests
  (are [args expected] (= expected (apply n-groups args))
    [20 5 15] 2
    [40 5 15] 3
  ))

It isn't clear what should be returned if there are multiple answers, for instance, when n-elems is 7.

Why is the expected answer for [1000 3 40] 25? All the piles would be equal then. Shouldn't it be 28?