Twinning by exchange of two statical units 4

a) 1.Rf2 Kb1 2.Kf3 Qh3#

b) 1.Rh2 Qe1 2.Rf2 Qc3#

The most economical helpmate. Miniature with chameleon echo mates shows also tempo moves by both sides: in a) by wK, in b) by bR. The roles of echanged bQ and bp are clear, they both block squares in mates and their position determines the play as bQ guards in both positions one of the prospective checkmates.

a) 1.Qxb4 Rc3 2.Qb3 Rxb3#

b) 1.Qg2 Rc7 2.Qxb7 Rxb7#

The same use of echanged units - they both block and they both guard one of vertical rook lines to b5. Annihilation of white force by bQ leading to the ideal mates is quite unexpected.

a) 1.Bd6 Bf2 2.Bb4 Sb2#

b) 1.Rh4 Bd6 2.Rd4 Se5#

Again the exchanged units block bK's flights, but the strategy is again more interesting than before. In a) two orthogonal lines to b2 are closed, in b) two diagonal lines to e5.

a) 1.Qxf3 Bh3 2.Qd5 Sd4#

b) 1.Qxc2 Rb1 2.Qc5 Se5#

Very usual use for twinned units. As they are of different colour, there is a wider set of potentially blocked/guarded squares than as with black units only. Whte pawn from a6 guards b7, from b6 guards c7. This determines the battery that must be fired. Other rear piece makes lateral move - Bh3 guards d7 only while Rb1 both b5 and b6 - this way wpb6 in b) allows model mate. Also, any piece at a6 prevents check on a-file, but this point seems to be of minor importance.

a) 1.Se6 f4 2.Rf2 Sb6#

b) 1.Re6 f3 2.Sf2 Rc5#

Position of wK in twins determines black piece playing Umnov move to f2, interfering with bBg1. This bishop mustn't move and this is secured by twinned bQ that keeps behind bB with respect to the wK. The play is finished by black dual avoidance on 2nd move.

a)
1.Kc5 Ra4 2.Bxc6 Qxc6#
1.Kxe5 Qxf3 2.Rd5 Rxd5#

b)
1.Kxc6 Rxb5 2.Bd5 Qxd5#
1.Ke4 Qxg3 2.Rxe5+ Rxe5#

At last some different use for thematical pieces. White pawn only prevents cooks and in reality doesn't play any constructive role in any of four phases. On the other hand, knight is captured in two solutions by bK and supports mating piece in other two solutions. Nice echo diagonal-orthogonal of pairs of different solutions.

a) 1.Sxe6 Rxe4 2.Sg7 Qa1#

b) 1.Sxe5 Bd7 2.Sg6 Qa6#

Both exchanged pieces block bK flights and guard mating lines. But the strategy is improved even more and the problem as a whole is very inspirative - echo diagonal-orthogonal of complicated line play.

a)
1.Kf4 f8S 2.Be3 Sxe6#
1.Kf6 f8B 2.Sg7 Be7#

b)
1.Kxd6 f8R 2.Rc5 Rxd8#
1.Kd4 f8Q 2.Sg5 Qf2#

Yes, bK stands in check in both positions, it is checked by thematicaly twinned white knight. White knight, of course, guards e5 in all 4 solutions, while bp blocks a square in both positions, what is used in mates with bK on 6th row.