Definition : "If a piece can move to the square it occupied in the diagram position, it must move to this back-home square. BackHome moves have priority over the virtual capture of the opponent king by any piece, i.e. checks are fairy. If more BackHome moves are possible, the side-on-move chooses which move to play. The BackHome square of a pawn which is promoted during the solution is the-initial-diagram-square of this pawn."
The fifth thematic tourney (TT5) of ChessProblems.ca, ending 31-XII-2013, required original chess compositions employing the BackHome fairy condition. For the Announcement and the Award please visit this link. You will find excellent material if you follow the link to the bulletin.
The condition is included in programs WinChloe 3.24 and Popeye 4.65 .
I will present here two helpmate problems of mine, one with normal pieces and one using a Grasshopper, where the BackHome condition is applied.
1.Rc3 Sc4 (the wS blocks the return path for the bRc3) 2.Re3 Se5 (the wS returns BackHome)
3.Rd5 Sd7 (the wS blocks the return path for the bRd5) 4.Rc5 Se5 (the wS returns BackHome)
5.Be6 Sg4 (the wS blocks the return path for the bBe6) 6.Bd5 Se5 (the wS returns BackHome)
The wS, visiting 3 different squares and then returning BackHome, blocks the BackHome path of three black units which block their King. The four black pieces go to their destinations one after another in strict order.
a) diagram, b) bGa4 to h8
1.Gd1 (the wG cannot return to a4) Rf1 2.Gg1 (blocks the return path of bRf1) Rf4 3.Kg5 Rxh4 (inhibits the BackHome move of the bK) 4.Gg6 Rh8 5.Gg4 Rg8+ 6.Kh6 (the bK makes a switchback BackHome) hxg4# (the wRh1 is in BackHome position, the check is valid, it is mate).
b) bGa4 to h8
1.Gh5 (the wG cannot return to h8) Rd2 2.cxd2 Kd3 3.d1=B (inhibits the BackHome move of the bK to c2) Ke4 4.Gxh3 Kf5 5.Ge6 Rxh4 (this is not a check) 6.Kh5 (the bK is not in threat) Rh1# (wR moves away from bK and makes a switchback to BackHome position to give check. Three pieces are cleared from the h-file to make this mate possible, and the promoted bBd1 is unable to interfere).
There are sacrifices, of bGg4 in (a), of wRd2 in (b).
There are reciprocal captures, wPxbG in (a), bGxwP in (b).