1.Nd4+ Ke1
1...Kd1 leads to 2.Qb1#
2.Qh2! Kd1!
2...Qf2 3.Nc2+ Ke2 (3...Kf1 4.Qh1+, 3...Kd1 4.Qh1+) 4.Qh5+ transposes to 4...Qf2
2...Qa6 leads to 3.Nc2+ Kd1 4.Nxe3+ Ke1 (4...Kc1 5.Qc2#) 5.Qd2#
Other moves lose the queen or allow 3.Qe2#
3.Qh7! Ke1!
White's threat is 4.Qb1#. 3...Kc1 leads to 4.Qc2#
3...Qe1+ leads to 4.Kb3 transposing to 6.Kb3 in the 4...Kd1 line
4.Qh4+
4.Qe4? leads to 4... Kf2 5.Qf3+ Kg1 6.Ne2+ Kh2 7.Qxf1 (stalemate!!)

The problem now branches into two main possibilities
a)4...Kd1
5.Qe4! Qe1+
6.Kb3 Qf2
6...Qd2 leads to 7.Qh1+ Qe1 8.Qh5+ e2 (8...Kd2 9.Nf3+; 8...Kc1 9.Qc5+ followed by Qc2# or winning the Black queen) 9.Nf3 and Black must loses his queen or allow 10.Qd5+ Kc1 11.Qd2+ Kb1 12.Qb2#
Other Queen moves lose the queen or allow 7.Qc2+ Ke1 8.Qe2#
7.Qb1+ Kd2
8.Qc2+ Ke1
9.Qc1#

b)4...Qf2
5.Nc2+ Ke2
5...Kf1 leads to 6.Qh1+ transposing to 7.Qh1+
5...Kd1 leads to 6.Qh1+ Qg1 (6...Ke2 7.Nd4#) 7.Qxg1+ Ke2 8.Nd4#
6.Qh5+ Kf1
6...Qf3 leads to 7.Nd4+ forking king and queen
7.Qh1+ Qg1
7...Ke2 leads to 8.Nd4#
8.Qf3+ Qf2
9.Nxe3+ Kg1
9...Ke1 leads to 10.Qd1#
10.Qd1+ Kh2
11.Ng4+, and white has a queen and king v. king situation.
