I'm puzzled

Another broken puzzle(s).

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lichess.org/training/10699

"Right" solution:
1.b4+ Ka4 2.bxc5+ Qc4 3.Qd1+ Ka5 4.Qd2+ Ka4 5.Nc3+ Ka5 6.Nd5+ Ka4 7.Nb6+ Kb3 8.Re3+ Qd3 9.Rxd3#

Really right solution ("puzzle failed"):
1.b4+ Ka4 2.bxc5+ Qc4 3.Nc3+
a) 3.... Kb3 4.Qd1+ Kxc3 5.Re3+ Qd3 6.Rxd3+ Kb2 7.Qc1#
(6.... Kc4 7.Rc1#)
b) 3.... Ka5 4.Qxc4 bxc4 5.Rb1 Rb7 6.Bxb7 * 7.Rb5#

Proof:
http://ru.lichess.org/WMJYLrNqptfM

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http://ru.lichess.org/training/25291
Right solution (checkmate in 9):
1.... Bxb6 2.Kh5 Rxb7 3....
Alternative (checkmate in 9, ignoring the opponent's bishop):
1.... Bxb6 2.Kh5 Bf2 3.... - is also a solution (variants are quite numerous)

Thanks.

http://ru.lichess.org/training/41182

Main solution:
1.... Qh4+ 2.Ke2 Nf4+ 3.Kf3 Bd5+ 4.Kxf4 Qf2+ 5.Qf3 Qxf3+ 6.Kg5 f6+ 7.Kh5 Bf7+ 8.Kh4 Qf2#

But on 4th move there are few equivalent (and semi-equivalent, 'N+1') branches. All equivalent and 'N+1' solutions are rejected ('puzzle failed').
'N+1'-solution:
A) 4.... g5+ 5.Kf5 Qh6 6.Qa4+ Kf8 7.Qa6 bxa6 8.e6 fxe6+ 9.Ke5 Qg7#
Equivalent solutions:
B) - accelerated (A): 4.... c6 5.Be2 g5+ 6.Kf5 Qh6 7.e6 f6 8.Rh2 Qg6#
C) 4.... 0-0 5.Bg2 g5+ 6.Kf5 Qh6 7.e6 fxe6+ 8.Ke5 Qf6#

Thanks.