Abstract. Let G be a graph. Denote by Lⁱ(G) its i-iterated line graph and denote by W(G) its Wiener index. Dobrynin, Entringer and Gutman gave a problem if there exists a nontrivial tree T and i≥3, such that W(Lⁱ(T))=W(T). In this paper, which is 6th and last of a series, we completely solve this problem.