a) diagram
1.Kd4! threat 2.Rb1 Kd2 3.Qh2#
1…Kb2(Kb3) 2.Rb1+ Ka3, Kc2 3.Qa8, Qh2#
1…b4 2.Qh2+ Kb3 3.Qa2#
b) wQh8→b8
1.Kd4! threat 2.Q:b5 and 3.Qb1#
1…Kb2(Kb3) 2.Q:b5+ Ka3, Kc2 3.Ra1, Qb1#
1…b4 2.Q:b4 d5 3.Qb1#
1…d5 2.Rb1 Kd2 3.Qh2#
c) bPd6→e4
1.Kd4! threat 2.Qg8 Kb2 3.Qa2#
1…Kb2(Kb3) 2.Rb1+ Ka3, Kc2 3.Qa8, Qh2#
1…b4 2.Qh2+ Kb3 3.Qa2#
d) bPb5→d3
1.Kd4! threat 2.Qb8 ~ 3.Qb1#
1…Kb2(Kb3) 2.Qb8+ Ka3, Kc2 3.Ra1, Qb1#
1…d5 2.Qb8! d2 3.Qb1#