Knight-wheel

Some chess problems are constructed with the aim of rendering certain tasks or maximum effects. A well-known example of such tasks is the knight-wheel. A knight, when placed near the centre of the board, is capable of making a maximum of eight moves, and if the piece plays all eight possible moves in turn during the course of a problem’s solution, the knight-wheel theme is produced. Usually the term knight-wheel is used in cases where a black knight carries out the thematic play. When a white knight makes the maximum eight moves instead, the task is called a knight-tour.

Problem 79, composed nearly a century ago, remains one of the best renditions of a knight-wheel. White starts with 1.Sf3!, to threaten 2.Sd2. This mate cuts off the queen’s guard along the d-file, allowing Black to subtly defend by shifting the knight away from d4, to create a potential flight on that square. The eight knight moves all bring about distinct white replies, as required by the theme. 1…Sc2 2.Qd3, 1…Sb3 2.Qxb1, 1…Sb5 2.Bxb7, 1…Sc6 2.Qd5, 1…Se6 2.Re5, 1…Sf5 2.Rg4, 1…Sxf3 2.exf3, 1…Sxe2 2.Qxe2. The first five variations are based on self-interferences – the knight closes a vital defensive line of another black piece – a type of error with more strategic interest than, say, a simple unguard. The latter error is seen in the by-play variation, 1…Rb2 2.Qxd4. This well-constructed work shows a wealth of good play in a position that is nonetheless pleasantly open and economical.

In Problem 80, the knight-wheel moves of the d5-knight remarkably serve a double function. In addition to working as defences that compel different white mates, the knight moves also act as the refutations of eight white tries. First note that set mates are already provided for the knight’s play: 1…Sxc3 2.Rb3, 1…Sb4 2.Rxb4, 1…Sb6 2.Rxb6, 1…Sc7 2.Rxc7, 1…Se7 2.Rxe7, 1…Sxf6 2.Rf7, 1…Sf4 2.Sd4, 1…Se3 2.Rf2. Now White has eight thematic tries, most of which generate a variety of threats, while a couple attempt to maintain the block position, but all are defeated by the black knight using different moves. 1.Qa7? (threats: 2.Qf2, 2.Rf2) Sb6!, 1.Qb8? (2.Qg3, 2.Sd4) Sc7!, 1.Qa5? (2.Qxd5) Se7!, 1.Qd8? (2.Qxd5) Sb4!, 1.Qa1? (2.Qf1) Sxc3!, 1.Bd4? (2.Rf2) Se3!, 1.f7? (waiting) Sf6!, and 1.Kg5? (waiting) Sf4! The key is the sole effective waiting move, 1.g5!, that leaves the set play unchanged.

A white knight-tour typically appears in the form of eight mating moves delivered by the knight, an effect that requires a battery set-up. Problem 81 demonstrates this idea with a bishop + knight battery, working against a busy black queen that sets off all the variations. The key 1.Rg4! threatens 2.Rg8, and to stop this mate the queen has to unpin the knight. The released knight then fires the battery in eight different ways, the selection of which depends on where Black puts the queen: 1…Qxd6 2.Sxd6, 1…Qxf6 2.Sxf6, 1…Qc5 2.Sxc5, 1…Qg5 2.Sxg5, 1…Qc3 2.Sxc3, 1…Qg3 2.Sxg3, 1…Qb2+ 2.Sd2, and 1…Qh2+ 2.Sf2. Also, 1…Qxe4+ 2.Bxe4.

Problem 82 poses an alternative of rook + knight batteries to achieve two complete knight-tours. After the try, 1.Rc8?, White’s threats are any move by the c6-knight. Each of the eight possible knight mates has to be individually forced, for the theme to be realized. 1…Ra8 2.Sb8, 1…Ra7 2.Sxa7, 1…Ra5 2.Sxa5, 1…Rxa4 2.Sb4, 1…Bd4 2.Sxd4, 1…Be5 2.Sxe5, 1…Be7 2.Sxe7, 1…Bd8 2.Sxd8, but 1…b5! refutes the try. The key 1.Rh3! leads to a similar tour by the other knight, whose multiple threats are separated by 1…Rh1 2.Sh2, 1…Rg1 2.Sxg1, 1…Re1 2.Sxe1, 1…Rd1 2.Sd2 1…Bd4 2.Sxd4, 1…Be5 2.Sxe5, 1…Bg5 2.Sxg5, and 1…Bh4 2.Sxh4. (1…Sc2 2.Rxc2.)

In Problem 83, White’s knight on d5 executes a tour by making seven tries and the key, where each try is defeated by a different move. When White shifts the knight, 2.Rd5 is threatened, but seven times Black has a foiling defence when the knight impedes a prepared mating move. That the tries all fail for a similar reason – White self-interferes on a line controlled by another white piece – greatly adds to the unity of the knight-tour. 1.Se3? Bg2! (2.Rxd3 stopped), 1.Sf4? Rd7! (2.Rh4 stopped), 1.Sf6? Rh5! (2.Bg7 stopped), 1.Se7? Sb6! (2.Bc5 stopped), 1.Sc3? Sb4! (2.Qa1 stopped), 1.Sb4? Sc3! (2.Qxc3 stopped), 1.Sb6? Se7! (2.Qxa7 stopped). Finally, the non-hindering 1.Sc7! solves, 1…Bg2 2.Rxd3, 1…Rd7 2.Rh4, 1…Rh5 2.Bg7, 1…Sb6 2.Bc5, 1…Sb4 2.Qa1, 1…Sc3 2.Qxc3, 1…Se7 2.Qxa7.