We study the mass splittings of Q1q2Q3q4 (Q = c, b, q = u, d, s) tetraquark states with chromomagnetic interactions between their quark components. Assuming that X(4140) is the lowest J P C = 1 ++ cscs tetraquark, we estimate the masses of the other tetraquark states. From the obtained masses and defined measure reflecting effective quark interactions, we find the following assignments for several exotic states: (1) both X(3860) and the newly observed Zc(4100) seem to be 0 ++ cncn tetraquarks; (2) Zc(4200) is probably a 1 +− cncn tetraquark; (3) Zc(3900), X(3940), and X(4160) are unlikely compact tetraquarks; (4) Zc(4020) is unlikely a compact tetraquark, but seems the hidden-charm correspondence of Z b (10650) with J P C = 1 +− ; and (5) Zc(4250) can be a tetraquark candidate but the quantum numbers cannot be assigned at present. We hope further studies may check the predictions and assignments given here.