Neutral Pieces Only

These are the best "instructions" I found on the Web about chess problems with neutral pieces only -- and one neutral King:

Now the question of the day: Is it such a bad idea to Go All The Way? That depends, right? How about chess problems with everything neutral? As for me, I am absolutely fascinated by them. Others, even hard-core fairy problemists, prefer not to touch such compositions at all. But are they really so alien? Let's start with a simple diagram to see what is allowed and what is not.

Though there are only neutral pieces on the board, we still have to think in black and white. That may be the first psychological barrier. It's important to know which side has the move.

a)

The nK must not go to e6 or g6 due to an illegal self-check (the nPf7 has to be considered to be black)! For the same reason nBh7 is not allowed. Neutral pieces can capture each other. Neutral pawns promote to neutral pieces. nKe4,e5,f4,f6,g4,g5; nBxf7; nPf8=nB,nN; nPxg8=nQ,nR,nB,nN are legal.

b)

This time, the nK can go anywhere he likes. The moves nKe6,g6+ are no self-checks! Of course, they are checks to the neutral king thereafter. He is then considered to be white and the nPf7 to be black. But that's not illegal, for it is White's turn and so the check is parried by moving the king away (e.g. nKf6, but not nKxf7) or by making a legal pawn move (nKe6: nPxg8=nN,nR; nKg6: nPf8=nQ,nR,nB or nPxg8=nB,nN).Legal moves are nK~(+); nBxf7; nPf6.

 Now, what I can't understand is: if the mate is legal, why the self-check is illegal? Isn't the mate a sort of self-mate, in neutral-pieces-only problems? Or, say, an attempted mate? :)

I composed a problem with these condition, but, alas, it contains the horrible self-check, and so it's without (legal) solution...

H#3

Circe

(Wannabe) Sol. 1. nBa1, nBc6 2. nBxb5 (npb2), nBd5+ 3. Kh8, b4#.

Is This Problem Correct?

Giuseppe Lucchesini

Inedito

Anti-Kings

h#4

The Anti-King is in check when not attacked by an enemy unit. So, This is my solution: 1. g5, Kh7 2. Rg8+, Kg6 3. Rf8+, Kf5 4. Re8+ Ke4#. Popeye does not "agree", and does not offer any solution... Am I wrong?