Fairy helpmates with echo diagonal-orthogonal 4

1...LOxf5-g4 2.Be6 LOxe6-d7#

1.Ke6 LOxd5-d4 2.Sd6 LOxd6-d7#

Less usual way of expressing echo diagonal-orthogonal: a set play and a solution. White locust jumps there and back again (hobbit). :-)

a) 1.Qxh4 Bd8(Rf6) 2.Qhxf6 Bxf6(Rh4)#

b) 1.Qxf6 Rf2(Bf4) 2.Qfxf4 Rxf4(Bf6)#

In both phases both white pieces return to their initial squares. Made possible thanks to Circe Parrain.

1.Bxe2(w) Bf3 2.Bxb3(w) Bxb7(b) 3.Bf3 Bd5#

1.Rxe2(w) Ra2 2.Rxb3(w) Rxa7(b) 3.Ra2 Ra3#

Here the Andernach chess allowed mixed switchbacks - a piece leaves it square, captures and then returns to the initial square having the different colour. 3x2 switchbacks together.

a) 1.Qf5 Bg6+ 2.Qd7 Bc7 3.Rf8 Rxe4#

b) 1.Qg7 Rg6+ 2.Qd7 Bd6 3.Bf5 Bxg8#

Madrasi typical motivation of the switchback: black queen temporarily closes a paralysis line and allows rearrangement of the initially paralysed pieces, then returns them to paralysed state.

1.Rf1 KAc1 2.Rf4 Be3#

1.Bd7 KAb5 2.Bf5 Rc5#

Here black pieces serve as a one-time hurdles for white kangaroos, after jumps in B1 they return and block. The mate is given by kangaroo over pinned black pieces and its piner.

1.RHf6 RHe6 2.BHh4 BHd7 3.RHg4 RHe3#

1.BHg6 BHh7 2.RHg4 RHh8 3.BHh4 BHf5#

This surely isn't switchback problem. Indeed, one is only in the second solution, while in the first solution the double hopper battery is fired by the move not returning to the initial square. But I couldn't resist temptation to include a problem by our judge. The other reason is that some reader may find the way to improve this position...