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:1 Rh1!
::1 …Bxh7...Bxh7, 2.Nd5# (unguards d5)
::1 …Bf7...Bf7, 2.Qf5# (interferes with rook’s guard of f5)
::1 …Be6...Be6, 2.e3# (interferes with rook’s guard of e3)
::1 …Bd5...Bd5, 2.Nxd5# (unguards d5)
::1 …Bxc7...Bxc7, 2.Rh4# (unguards h4)
::1 …Be7...Be7, 2.e3# (interferes with rook’s guard of e3)
::1 …Bf6...Bf6, 2.Qf5# (interferes with rook’s guard of f5)
::1 …Bg5...Bg5, 2.Qh2# (blocks king’s flight to g5)
::1 …Bh4...Bh4, 2.Rxh4# (unguards h4)
::1 …Rf7...Rf7, 2.Nd5# (interferes with bishop’s guard of d5)
::1 …Rf6...Rf6, 2.Rh4# (interferes with bishop’s guard of h4)
::1 …Rf5...Rf5, 2.Qxf5# (unguards f5)
::1 …Re7...Re7, 2.Rh4# (interferes with bishop’s guard of h4)
::1 …Re6...Re6, 2.Nd5# (interferes with bishop’s guard of d5)
::1 …Re5...Re5, 2.Qg4# (blocks king’s flight to e5)
::1 …Re4...Re4, 2.fxe4# (allows pawn capture discovering check)
::1 …Re3...Re3, 2.Bh2# (blocks king’s flight to e3)
::1 …Rxe2...Rxe2+, 2.Nxe2# (allows capture on unguarded square e2)
::1 …c3...c3, 2.Nd3# (unguards d3)
The thematic approach to solving is to notice then that in the original position, Black is already almost in zugzwang. If Black were compelled to play first, only Re3 and Bg5 would not allow immediate mate. However, each of those two moves blocks a flight square for the black king, and once White has removed his rook from h2 White can put some other piece on that square to deliver mate: 1...Re3 2.Bh2# and 1...Bg5 2.Qh2#.
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