Helpmates in two with grasshoppers and nightriders 10

1.b1R f8S 2.Rb7 Sd7#

1.b1B f8Q 2.Bd3 Qb4#

Normal AUW with use of grasshoppers. Model mates.

a) 1.Qa6+ Ga3 2.Qg6+ Ga8#

b) 1.Qe2+ Gb2 2.Qe5+ Gg2#

c) 1.Qc4+ Gb3 2.Qxf4+ Ge6#

Nice analogy in black play, all 6 moves are checking. It is true that in c) position the motivation for Qxf4 is different from other parts and thus the analogy isn't pure, but I like it anyway.

Unfortunately cooked in both a) and b) parts:
1.Qe3 Ge2 2.Qe5 Gg2#
It is exactly this position that appeared in magazine, where is the problem?

1.Qg3 Gg2 2.Qh4 Gf1#

1.Qg4 Gg3 2.Qh4 Gb3#

1.Qg5 Gg4 2.Qh4 Gf5#

Three analogic solution with pure mates - their economy is questionable as grasshopper on g-file takes only passive role.

a) 1.Gxh5 Rh8 2.Ge2 Rh1#

b) 1.Gxb6 Rb8 2.Gf2 Rb1#

c) 1.Gxc6 Rc8 2.Gg2 Rc1#

Again three pure mates, this time model mates! Nice point is also capture of white grasshopers, this way the line for white rook is cleared.

1.Bh7 Ng6 2.Nd2 Gg4#

1.Rc8 Nc7 2.Qd2 Ga7#

Complex strategy. To allow mates, black must place something on d2 to cover d3 and also move away Bg6/Rc7. But white lacks neutral moves - this determines order of black moves and exact arrival squres h7/c8 providing safe tempo move for white nightriders. Also arrivals on d2 cannot be exchanged for Qd2/Nd2 due to guard on mating line in the case of wrong piece entering d2. Note the fact that white cannot play Nxc7 and Gg4 in the same solution due to pin on 1st row and Nxg6 and Ga7 due to guard on a7 from Ga2. Great echo diagonal-orthogonal and - what is not trivial - model mates.