Madrasi Rex Inclusiv with active kings 1

1.Kb7 2.Kc6 3.Kd5 4.Ke4 5.Kf3 6.Kg2 7.Kxh1(Ra8) 8.Kg2 9.Kf3 10.Ke4 11.Kd5 12.Kc6 13.Kb7 14.Kxa8 15.Kb7 16.Kc6 17.Kd5 18.Ke4 19.Kf3 20.Kg2 21.Kf1 g2#

White wants to get mated on f1, however, Rh1 prevents that in two ways: it guards f1 and can move instead of pg3. So White has capture it - twice as the first capture results in rebirth. This gives pendular movement of white Rex Solus along the diagonal of chessboard.

1.Kd5! zz
1...Kxe6 2.c8B#
1...Kc6 2.c8R#
1...Ke8 2.c8Q#
1...Kd6 2.c8S#
1...Kc8 2.gxf7#
1...Sf6 2.Kc6#

Convincing duel presentation of AUW combined with "our theme". Black king has 5 flights, after the key by wK 3 of them lead to mates using paralysis of bK, after 1...Kxe6, Kc6, Kd6. White always promotes the piece that can check then, keeping in mind that queen promotion is for the time being ruled out by possible 2...Sf6! When bK steps to e8, closes 8th rank and the necessity to guard d7 forces queen promotion. In the by-variation 1...Sf6 white can mate using the queen on board, however it means he has to paralyze bK while opening royal battery. Well done.

1.Kg8 2.Kf8 3.Ke8 4.Kd7 5.Rf8 6.Rf7 7.Qe2 8.Qg2 9.Rf3 10.Kc6 11.Rg3 Qc7#

Multiple closure of lines: 4.Kd7 closes bQ-wK, 6.Rf7 closes bQ-wQ (then bQ must find precise way to g2), 9.Rf3 closes bQ-wK, 10.Kc6 closes bQ-wK in anticipation and 11.Rg3 closes bQ-wQ.

1.Qb7 Kf2 A 2.Rd7 B Bxc4#
    1...Rd7 B 2.Ke2 C Bxc4#
1.Qe8 Ke2 C 2.Bd7 D Rxf6#
    1...Bd7 D 2.Kf2 A Rxf6#

Less usual form of helpmate with bifurcation of the solution flow in both the black and white first moves. The strategy is clear. To mate by bishop, two bishop bent lines should be closed, one rook line must be deactivated and bK must be paralysed. 1.Qb7 closes Bc8-a6-c4, then either white or black rook have to enter d7. In the meantime kings paralyse each other. The necessity to let some lines active (nearby kings) and closed (directed through d7) contributes crucially to the formation of W&B formal cycle of moves.

1...Kb5 2.Qd7#
1...Kc5 2.Qd5#

1.Kb3! zz
1...Kb5 2.Kxa4#
1...Kc5 2.Kxb4#

In the set play of this mutate, black king self-paralyzes and white mates by queen. The key is very surprising as it moves king away and thus black king does not self-paralyze. It however walks to squares where he can be checked by capture of black piece paralyzing the on attacking square of bK. These checks prove to be lethal = mates, as wK himself paralyzes bK.