To be fair, I tried solving this manually.

Qb1 works.

Basic idea - We see that the White king cannot move. All that is needed is to give it a check. But where to give it a check from? The Black queen guards many key squares like h4, e3, c3, e1. Thus, White should try to find other squares. Qb1 threatens mate with Qb4+.

This is what I calculated -

1...exd5 2. Bxd5#
1...e5 2. Qb4#
1...b4 2. Qxb4#
1...h1=Q 2. Qb4#
1...Qxa3 2. c3!#
1...Qe1 2. Qxe1#
1...Qe3 2. Rxe3#
1...Qb3 2. cxb3#
1...Nxg6 2. Qb4#

I also confirmed with a computer that Qb1 is correct.

To be fair, I tried solving this manually.

Qb1 works.

Basic idea - We see that the Black king cannot move. All that is needed is to give it a check. But where to give it a check from? The Black queen guards many key squares like h4, e3, c3, e1. Thus, White should try to find other squares. Qb1 threatens mate with Qb4+.

This is what I calculated -

1...exd5 2. Bxd5#
1...e5 2. Qb4#
1...b4 2. Qxb4#
1...h1=Q 2. Qb4#
1...Qxa3 2. c3!#
1...Qe1 2. Qxe1#
1...Qe3 2. Rxe3#
1...Qb3 2. cxb3#
1...Nxg6 2. Qb4#

I also confirmed with a computer that Qb1 is correct.

To be fair, I tried solving this manually.

Qb1 works.

To be fair, I tried solving this manually.

Qb1 works.

Basic idea - We see that the White king cannot move. All that is needed is to give it a check. But where to give it a check from? The Black queen guards many key squares like h4, e3, c3, e1. Thus, White should try to find other squares. Qb1 threatens mate with Qb4+.

This is what I calculated -

1...exd5 2. Bxd5#
1...e5 2. Qb4#
1...b4 2. Qxb4#
1...h1=Q 2. Qb4#
1...Qxa3 2. c3!#
1...Qe1 2. Qxe1#
1...Qe3 2. Rxe3#
1...Qb3 2. cxb3#
1...Nxg6 2. Qb4#

I also confirmed with a computer that Qb1 is correct.