Mate with two Knights on the edge of the chessboard

There is a beautiful problem by the French poet and novelist Alfred deMusset since 1849, which shows a mate with two Knights on the edge of the chessboard. In order to achieve such a mate, one must have another black piece on board, which may disappear in the final picture of mate, or a pawn not too advanced (see Troitsky line).

Problem-737 Alfred deMusset La Regence, 1849
1s2k1K1/7R/8/4S3/6S1/8/8/8 (4 + 2)	#3, Mate in three moves 1.Rd7! [2.Sf6#] Sxd7 2.Sc6 Sf6+ 3.Sxf6#
final picture of mate

I like this problem and I have composed, for a recent composition tourney, a helpmate two-mover twin.
On the first of the twins, White manages easily to force a mate on the cooperating Black with two Knights on the edge of the chessboard, (making two simple moves and two captures).
But on the second problem a black Rook is placed on board and inhibits the mate of the first twin! White, more difficult now (with four captures, pins, unpinnings and removals of guards), manages again to achieve the mate with two knights, but in another edge of the chessboard!
For a two-mover, I consider it nice, (and it is irrelevant that the judge saw the two solutions unsimilar and gave no distinction). Of course, the two fairy conditions were very helpful TakeAndMake (the capturing piece makes one move with the way of the captured piece. Example: if a Rook captures a Knight, the Rook must make one more step as Knight) and Anti-TakeAndMake (the captured piece is not removed from the game but it makes one move without capturing anything on the arrival square.
Final result, with the two fairy conditions combined, is a situation described recently as Bulgarian billiard.
Example: (1) if a Rook captures a Knight, the Rook must make one more step as Knight, and the Knight stays on the board and makes a move itself as a Knight. (2) if a Knight captures a Bishop, the Knight must make one move as Bishop, and the Bishop stays on the board and makes a move itself).

Problem-738 Manolas Emmanuel original
8/1K6/8/6bS/8/5S2/5k2/1b6 (3 + 3)	h#2, helpmate in 2 conditions TakeAndMake, Anti-TakeAndMake Twin a) Diagram, b) +bRc6, addition of a black Rook a) 1.Bg6 Sg3 2.Kxg3(Kh5;Se4) Sexg5(Sf6;Bh6)# b) bRc6 1.Kxf3(Ke1;Sd2) Kxc6(Kc1;Rh6) 2.Rxh5(Rf4;Sg3) Sxb1(Sd3;Ba2)#
final picture of mate a	final picture of mate b

We have composed, together with the Italian Vito Rallo, problems with similar final mates, but using another fairy condition, Andernach (the capturing piece, changes colour).

Problem-713 Manolas Emmanuel and Rallo Vito Variantim, April 2013
8/8/8/8/8/1K2SP2/4k3/4s3 (3 + 2)	#3 condition Andernach 1.Sxf3(=wSf3) Sd4+ 2.Kd2 Ka2 3.Kc1 Sb3# 1.Kd2 Sd5 2.Kd1 Kb2 3.Sxf3(=wSf3) Sc3# Ideal Mates, Chameleon.
final picture of mate in first solution	final picture of mate in second solution
Problem-739 Manolas Emmanuel and Rallo Vito Julia's Fairies Νο.248, February 07, 2013
8/2K1kss1/8/5PG1/8/8/8/8 (3 + 3) (Grasshoppers: f5 + 0)	#3 condition Andernach Grasshopper on g5 1.Kf8 Kd7 2.Sxf5(=wSf5) Sh6 3.Sxg5(=wSg5) Se6# 1.Ke8 Ge5 2.Sxe5(=wSe5) Sg6 3.Sxf5(=wSf5) Sd6#
final picture of mate in first solution	final picture of mate in second solution