Improving a fairy helpstalemate – Part 2

In the previous column, we looked at a helpstalemate featuring a royal knight and some potential ways to enhance the problem. First, by utilising the set play inherent in the position which contains a queen promotion, we saved a couple of units while preserving the triple-promotion theme. Then we attempted to add a knight-promotion set play by reinserting the white king, but the resulting position was spoiled by a dual. So would it be possible to compel a single move order in this set play? One option is to replace the orthodox d7-pawn with a royal one, a unit that is susceptible to check like its black knight counterpart. Given that a royal pawn promotes to a royal piece, an immediate 1…d8=rS in the set play would be illegal because d8 is attacked by the black knight. Hence the pawn promotes only on the second move, after the black piece has moved to a5.

Two issues arise from this scheme, however: (1) the white king can no longer be used because of a convention against a player having more than one royal unit, and (2) the queen-promotion set play, intended to start with 1…d8=rQ, is rendered illegal as well. On the first issue, a good replacement for the white king is a fairy piece known as the wazir; it's a close relative of the king that moves only one orthogonal step at a time. Such a wazir on c3 would (like the king) guard b3 and c4 and so help to trap the royal knight on a5 (though unlike the king, it wouldn’t control b4 or any diagonally-adjacent square). Now we can test various placements of the wazir that are one step away from c3, and see if any of them would also resolve the second issue, the lack of a queen-promotion phase. Adding the wazir on c2 (where we put the king in Version B) produces numerous cooks in which the royal knight is stalemated on a2, e.g. 1.rSb4 d8=rQ/rR/rB 2.rSa2 rQb6/rRb8/rBe7 (these lines were ineffective with the king on c2 because then 1.rSb4 would check). If we place the wazir on d3, the resulting position (diagram C) comes very close to fulfilling our aims. The set play 1…Wc3 2.rSa5 d8=rS and two original solutions (rook and bishop promotions) all work as intended, and the wazir’s placement has generated new play that is precise and involves a queen promotion. But two such solutions have been created – 1.rSa7 d8=rQ 2.rSb5 rQe7 and 1.rSb4 d8=rQ 2.rSc2 rQa5 – one too many for our purposes!

Besides deploying a royal pawn, is there another way to force the move order of the knight-promotion set play? Yes, if the white unit whose function is to control b3 and c4 happens to be attacking a5 initially, then this unit must move first before the pawn promotes, so as to allow the royal knight to access that square. A white king cannot handle this task, however, because the only square from which it could both attack a5 and move to c3 is b4, but this square is guarded by the black knight. So let's return to the idea of using a wazir, and note that it has an alternative square from which to control b3 and c4, namely b4 (where unlike the king it maintains the stalemate by not checking the royal knight on a5). Now by adding the wazir on b5 or a4, it does the job of attacking a5 while being able to move to b4. If placed on b5, the piece would cause many cooks, including even a one-move solution, 1.rSa7 Wb6/Wc5. But if the wazir starts on a4, the ensuing play seems accurate while meeting all of our requirements (see diagram below). 

The knight-promotion set play is dual-free: 1...Wb4 2.rSa5 d8=S. Since only a conventional pawn is needed, the queen-promotion set play becomes viable again: 1...d8=Q 2.rSa7 Qe8. The full-length solution with the bishop promotion works as before: 1.rSe7 d8=B+ 2.rSg8 Bg5. But what about the rook promotion? The original solution of 1.rSa5 d8=R 2.rSb7 Rd5 is now prevented by the wazir attacking a5, but in a remarkable stroke of luck, by also guarding b4 the piece has enabled another precise solution that necessitates a rook promotion: 1.rSb8 d8=R+ 2.rSa6 Rc8! Besides completing the Allumwandlung, this version of the problem differs from the original in three of its four phases (adding the knight promotion while changing the queen and rook promotion solutions). Consequently, I think it can be considered as a new problem. 

Improving a fairy helpstalemate – Part 1

5 Nov. 2016