Triple avoidance in helpmate 1

1.Be5 Bc4+ (Bxe4?, Bb3?) 2.Kd1 Sfe3#

1.Bg5 Bxe4 (Bb3?, Bc4+?) 2.Qd1 Sg3#

1.Sf5 Bb3 (Bc4+?, Bxe4?) 2.Kd3 Sf4#

To mate, white has to engage his bishop. That is why Black has to upin him. There are 3 possible indirect upinning moves closing the 4th rank (positive motif). However all of them guard 2 out of 3 possible mating squares e3, g3, f4 in mating finals, effectively making choice of 1st white move unambigous.

1.Rf3 Se5 (Sb4?, Sd4?) 2.Sxe7 (Sh6?, Sf6?) Sg4#

1.f3 Sb4 (Sd4?, Se5?) 2.Sh6 (Sf6?, Sxe7?) Sd5#

1.Sf3 Sd4 (Se5?, Sb4?) 2.Sf6 (Sxe7?, Sh6?) Sf5#

White has to do 2 moves with king to mate. That is why Black has to unpin him in the first move (positive motif). Unpin moves unblock flights (negative motif), choosing the 1st white move. However there is further choice of 2nd black move as it turns out that Black lacks free moves and he must move Sg8, his moves guard 2 of 3 mating squares.

1.Qe7 Sxe7 (Sd6?, Sb6?) 2.Sdf5 (Shf5?, Rf5?) Sc6#

1.Qb5 Sd6 (Sb6?, Sxe7?) 2.Shf5 (Rf5?, Sdf5?) Sxf7#

1.Qd7 Sb6 (Sxe7?, Sd6?) 2.Rf5 (Sdf5?, Shf5?) Sxd7#

Similar to and different from the previous problem. The first queen moves unpin knight and any move of queen allows 3 continuations. But from among 5 possible moves, Qc6+ is a check, and Qe6 guards all 3 potential mating squares c6, d7 and f7. 3 remaining moves all guard exactly 2 of 3 moves, making the choice of 1st white moves. But! Queen guards 3 potential mating squares already in the diagram position. Consequently, some people do not consider this to be trial avoidance as black motivation might be read as unpin AND unguard, with no negative motif.

1.d1S! Re4 (Bc3?, Rc3?) 2.Kxd5 Re6#

1.d1R! Bc3 (Rc3?, Re4?) 2.Kc5 Be5#

1.d1B! Rc3 (Re4?, Bc3?) 2.Ke5 Rc6#

Finally no unpin in the first black move. Black rather waits for White to close line allowing move of bK to 5th rank. Lack of waiting moves forces promotion of bPd2 and these avoid 2 out of 3 continuations by guarding.

1.Qg2 Bf5 (Bg4?, Se5?) 2.Qxg5 Qf1#

1.Qb5 Bg4 (Se5?, Bf5?) 2.Qxg5 Qf3#

1.Qg4 Se5 (Bf5?, Bxg4?) 2.Qxg5 Sd3#

And now for something completely different... Black strategy is simple, queen unguards all potential mating squares and lines and blocks g5 in all solutions. But it turns out that the precise routes to g5 should not be in conflict with white manoeuvres. Qg2 pins temporarily Sc6 and Bg4 would close queen line to g5, Qg4 should not be captured and closes bishop line to f5 and finally line of Qb5 to g5 should not be closed by Se5 and Bf5 moves. Refreshing!

1.Qf5 c8Q (cxd8Q?, cxb8Q?) 2.Sg6 Qxf5#

1.Qe6 cxd8Q (cxb8Q?, c8Q?) 2.Sd3 Qd4#

1.Qd7 cxb8Q (c8Q?, cxd8Q?) 2.Sfe6 Qe5#

Any diagonal move of bQ allows 3 queen promotions of pc7 (do you remember 11th TT CCM dedicated to queen promotions?), but again 2 of them are always avoided. The motivation is not very unified, but this did not seem to be the aim of the author.