The Grasshopper and the Nightrider

Chess problems that involve fairy pieces with unconventional moves are rarely featured on this site. Since such pieces enable interesting effects and themes not seen in orthodox problems, I’d like to give them a short introduction here. We will look at the two most popular fairy pieces, the grasshopper and the nightrider, both invented by T. R. Dawson a century ago.

The grasshopper moves along queen-lines but only by hopping over one piece (of either colour) and landing on the square immediately beyond. In the first diagram, the grasshopper on a7 has three legal moves: it can go to a3 by hopping over the black king, and similarly it can access d7 and d4 by using the pieces on c7 and c5 as hurdles. If there are no pieces standing on the same line as a grasshopper, it would be immobile. The nightrider is an enhanced knight; it’s able to make any number of knight steps in a straight line as one move. The nightrider on c7 can thus move to d5 or further along the same line to e3 or f1, for instance. Analogous to the rook and the bishop, the nightrider is blockable along the line it travels, so if a piece were on e6 it would stop the c7-nightrider from going to g5.

In this miniature, Black’s king is confined by the three white pieces on the c-file. The remaining white grasshopper is hence a good candidate to be the mating piece, and it makes the key 1.Gd7! to prepare an attack on the diagonal. Now if another white piece were to move to b5, it would enable the grasshopper to check (an “anti-battery” effect), though neither 2.Nb5 nor 2.Rb5 is threatened because these moves would cause an interference between the two line-pieces and create a flight for the black king. Because of zugzwang, however, Black is forced to self-block with the grasshoppers, thereby allowing these white moves to work: 1…Ga5 2.Nb5 and 1…Ga3 2.Rb5. The mutual interference between the two white pieces – a white Grimshaw – thus occurs in the two mating moves, an idea that can’t be shown so neatly, if at all, in an orthodox directmate.

The next example illustrates a convention relating to pawn promotion in fairy problems. The rule is that it is legal to promote to a fairy piece of any type that exists in the problem diagram. Therefore in the following position, the players may choose to promote to a grasshopper or a nightrider, in addition to the regular pieces.

In this helpmate, the black king has one accessible flight on a2, while a1 and c2 are guarded by the g4-nightrider and c1 by the h6-grasshopper. White aims to promote the g7-pawn to a grasshopper and use it to mate on b3 – a placement that activates the c4-grasshopper’s control of a2. But initially a promotion on g8 would be an illegal self-check due to the a8-grasshopper; furthermore, the b6-grasshopper is protecting the mating square b3. To deal with these obstacles in just two moves, Black uses the queen to cut off each grasshopper in turn: 1.Qe8+ g8=G 2.Qb5+ Gb3. The first queen check helps to legalise the promotion move, but the promoted grasshopper is left pinned. Next the queen not only unpins the grasshopper but also opens the rank again for the a8-grasshopper to give a discovered check, and White answers the check by vacating g8 – a curious form of cross-check. For part (b), the black rook starts on b3, meaning a2 is already guarded by the grasshopper on c4 while c1 is no longer controlled by the one on h6. To compensate, White plans to promote to a nightrider and mate with it on d2, where it would reactivate the h6-grasshopper. Paralleling the first solution, the black queen helps the white pawn to promote, and then interferes with the h2-grasshopper which is defending d2: 1.Qf8+ g8=N 2.Qf2+ Nd2.

Chinese pieces: Pao, Vao, and Mao

7 Aug. 2023