Fairy twomovers with multiple threats 3

1.Qc6! th. 2.Re4#, Bc3#
1...Rxc6 2.Bd2(Qe4)#
1...Bxc6 2.Re1(Qc4)#
1...Qxc6 2.Rd7(Qb6)#
1...Sxb4 2.Qc4(Bb2)#
(1...Qxe7 2.Qb6(Rd7),Re4(Re8),Bc3(Rf6)#
1...dxe7 2.Re4(Re8),Bc3(Rf6)#)

The key is quite strong, doing some guarding (d5, c3) as well as line closing (Nowotny). Thus two threats are created and any capture of wQ defends both. Captures by Nowotny pieces lead to mates with wB/wR causing rebirth of wQ along the closed line, capture by bQ allows double check mate. The additional defence by bS unblocks and capures, but allows another specific mate.

1.RLxf5-f6! A th. 2.RLxe5-e6#, RLxd5-d6#
1...bxc5(g4) a 2.RLxe5-e6# B
1...bxa5(e4) b 2.RLxd5-d6# C

1.RLxe5-e6! B th. 2.RLxd5-d6#, RLxf5-f6#
1...bxc5(f4) a 2.RLxd5-d6# C
1...bxa5(d4) b 2.RLxf5-f6# A

1.RLxd5-d6! C th. 2.RLxf5-f6#, RLxe5-e6#
1...bxc5(e4) a 2.RLxf5-f6# A
1...bxa5(c4) b 2.RLxe5-e6# B

White wants to move two rook locusts away from the first line for mate by PAh1. Moving one of rook locusts threats removing any of the remaining two, however this also means captures of black pawns. Black half-defences then place reborn pawns either on the possible rook locust lines, preventing moves, or on the lines of black bishops, causing the need for one of locusts to stay on the first line. This creative mechanism leads to complete Kiss cycle, with cyclic double threats.

a) 1.g8S? th. 2.c8B#, c8S#
1...Bf8!

1.c8S! th. 2.g8B#, g8S#

b) 1.c8S? th. 2.g8B#, g8S#
1...Bd8!

1.g8S! th. 2.c8B#, c8S#

There are two potential critical squares for the SAT mates here, namely d8 and f8. For both of them three guards have to be removed: both rooks and one of pawns.

In both positions bishop promotions as tries allow immediate move by black rooks therefore they are not so interesting.

But knight promotions merit the further analysis as they do not allow anything new, the black bishop is mobile already in the diagram positions. Knight promotion on g8 prevents move 1...Bd8, while promotion on c8 prevents 1...Bf8. The placement of the bQ decides which pawn has to be moved first.

1.Rc5? th. 2.Rb4# A, Rb3# B
1...Gxc5 a 2.Rxb5# C
1...Nd1 2.Rc6#
1...Nf1!

1.Nc5? th. 2.Rxb5# C, Rb4# A
1...Gxc5 a 2.Rb3# B
1...Nd1 2.Nxd3#
1...Bf1!

1.Bc5! th. 2.Rb3# B, Rxb5# C
1...Gxc5 a 2.Rb4# A
1...Nd1,Nf1 2.Bxd4#
1...Ge1 2.Rc1#

There is triple white Grimshaw on c5 (in the style of 8th TT CCM), leading to cycle of double threats by arrivals of wR on b3, b4 and b5 (of course, withdrawal along the 1st line is skilfully prevented by wK). Capture on c5 by grasshopper (it is important to use grasshopper to prevent additional black guard in all phases) leads always to the remaining mate in the Ukrainian cycle style (compare to Anticirce problem with the same theme).

The nightrider defence prevents wR from leaving b1 completely, but at the same time removes black guards from three squares at once - d5, d3 and d4 - leading to change of the second mate.

Very convincing SAT twomover in my view.

1.Bc5? th. 2.Sg6# A, Bf1# B
1...S3xc5 a 2.Sf7# C
1...S7xc5 b 2.Sb6# D
1...Sb6!

1.Rc5! th. 2.Sf7# C, Sb6# D
1...S3xc5 a 2.Sg6# A
1...S7xc5 b 2.Bf1# B

In this problem there is "only" ordinary white Grimshaw, but both lines are directed to a pair of potential flights of bK: Ba3 to d6 and e7, Ra5 to d5 and f5. Closing one of lines means thus double threat. Black knight defences capture interfering pieces, thus defend by possibility to open lines again. But the other piece is thus removed and threat mates from the other phase reappear. There is dual avoidance by opening Qd2 to d5 and d5, and by opening Gc8 to f5 and Rc7 to e7. After the dust settles, the Odessa theme with the same defences in both phases is clearly shown.

Note also the natural refutation and skillful determination of mating moves: Qh7 is nailed to h7 by wK flight, Bf1# cannot be replaced by Bh3+ because of Kf7 move and Sb6# has to close Ga6-d6.

One of the best SAT problems I have seen so far.

a) 1.Sc5! th. 2.Bxc3#, Sxd3#, Sxb3#

b) 1.Sc5! th. 2.Bxc3#, Sxb3#, Kb1#

c) 1.Sc5! th. 2.Sxd3#, Sxb3#, Kb1#

d) 1.Sc5! th. 2.Bxc3#, Sxd3#, Kb1#

The key is the same in all four positions, but the threats are not. Position of bS determines what is not a threat: Se3 guards d1, Se1 guards d3, Sb5 guards c3 and finally Sd2 guards b3. Maybe too mechanical, but it is a cycle of triple threats out of four possible in the meredith form after all.

1...Rexd2 2.Kg7(Pe3)#
1...Rcxd2 2.Bg8(Pc3)#
1...Sc~ 2.Q(x)e5#

1.Qe7? th. 2.Qc5#
1...Sxe7 2.Bf5(Qc5)#
1...Sb3!

1.Qd7! th. 2.Sd~#
1...Rexd2 2.Qe8(Pe3)#
1...Rcxd2 2.Qc8(Pc3)#
1...Sb8, Se5, Sxb4 2.Qa7#

There is a change of two mates between set play and solution after rook defences. They both capture Pd2 which is then transported to e3 and c3 respectively, depending on the defending rook. The change is motivated by guard of e4 and e5 (White can withdraw king and bishop in the set play) and ability of wQ to transport the pawn upwards. The try only underlines that capturing strong pieces in Circe Parrain is quite weak play. Non-capturing moves can be much stronger.

And why the problem is here? Because in the solution there are six threats. More coincidental, but well... you can try to do better.