Classic four-piece problems – Part 1

Problem positions with few pieces tend to be more enticing to solve, a natural preference that is happily compatible with the principle of economy of force in chess composition. The latter states that the amount of material used to show a problem’s idea should be minimised, with all non-essential pieces removed. Favouring economical positions is also reflected in how they are specially categorised: a miniature contains no more than seven units, while the German term wenigsteiner denotes a problem with four units or fewer. At the extreme end of the scale, employing just four pieces might seem too limiting to yield high quality content, but in fact skilful composers can incorporate advanced themes in such super-light problems. Let’s look at some of the best examples which have attained classic status.

In this four-part progressive twin problem, each new position for solving is derived by making a single adjustment to the previous one. For part (a), the black king has only one escape square on d8, hence a queen or rook promotion would cause stalemate. The key 1.b8=S! provides for the flight-move, 1…Kd8 2.Qd7. Part (b) requires a different underpromotion, 1.c8=B!, though the resulting variation is the same, 1…Kd8 2.Qd7. Part (c) is solved by 1.c8=Q!, which forces 1…Kd6 2.Qfc5. Lastly in (d), 1.c8=Q? would be stalemate, and 1.c8=B? Kd8 2.Qf8 but 1…Ke8! refutes; so 1.c8=R! Ke6 2.Re8. White carries out all four types of promotion, to bring about the evergreen Allumwandlung theme. By coincidence, Werner Speckmann published a similar four-unit AUW problem at the same time (December 1963): P1151009. Speckmann’s version is more widely quoted, probably because it has better variety without any repeated variations.

The subtle key 1.Ke4! serves two purposes; the king not only guards f5 to support a queen check on that square, but also vacates the long diagonal for the bishop. Thus, not 1.Ke5? Kh7! and curiously the black king escapes to the corner, as 2.Qf7+ Kh8 3.Bc3 is ineffective. After the correct start, 1…Kg5/Kh5 2.Qf5+ Kh4 3.Be1 and 2…Kh6 3.Bf8 show a pair of echo model mates, where the two mating configurations reflect each other. If 1…Kh7, then 2.Qf7+ Kh6 3.Bd2 displays the same formation again but shifted up the board, to give a third echo mate, though 2…Kh8 3.Bc3 brings a distinct arrangement (not a model mate since g7 is doubly guarded). Good coordination by the queen and bishop produces two pairs of sub-variations, in which the bishop delivers mates from four different squares.

The next problem has an unbelievable starting move, but first we examine why the alternatives fail. White begins by shifting the knight, to permit a promotion by the third move. A simple placement that makes no further use of the piece, like 1.Sf6?, is countered by 1…Ka7! 2.d7 Ka6 3.d8=Q Ka7. 1.Sb6+? seems better because it allows 1…Ka7 2.d7 Ka6 3.d8=Q Ka7 4.Qa8, but 3…Ka5! refutes. 1.Sc5? controls a6 and handles 1…Ka7 with 2.d7 Kb8/Ka8 3.Kb6 Ka8/Kb8 4.d8=Q, but now 1…Kb8! 2.d7 Ka7 and 3.d8=Q/R stalemates (or 2.Kb6 Kc8 3.d7+ Kd8). The startling key 1.Sb8! also attacks a6, so that 1…Ka7 is likewise answered by 2.d7 Kxb8/Ka8 3.Kb6 Ka8/Kxb8 4.d8=Q. The difference is that 1…Kxb8 assists White by removing the knight, then 2.d7 Ka7 3.d8=Q doesn’t stalemate (3.d8=R also works), 3…Ka6 4.Qa8/Qb6; or 2…Ka8 3.Kb6 Kb8 4.d8=Q.

It’s well-known that mating with K+R vs K involves zugzwang, and the plan here is to capture or block the pawn at the right moment to force the black king to a worse square. However, the black pawn turns out to be a pesky defender, and White needs to be precise to neutralise it. For instance, 1.Rf6? Kc1! 2.Rb6 f5, or 1.Rc8? Ke1! 2.Rf8 Kf2. Furthermore, two thematic tries (labelled [A/B]) by White and their respective refutations by Black (labelled [a/b]) generate an interesting formal pattern, when these four moves reappear after the key. 1.Rc5? [A] is defeated by 1…f6! [a] 2.Rf5 Kc1 3.Rb5 f5 4.Rxf5 Kb2, and 1.Rc4? [B] is defeated by 1…f5! [b] 2.Rf4 Kc1 3.Rb4 f4 4.Rxf4 Kb2.

The key 1.Rc7! threatens 2.Rxf7 (not stopped by 1…Ke1 2.Rxf7 Kd1 3.Rf1). Now 1…f6 [a] compels 2.Rc5 [A] f5 3.Rxf5 Kc1 (3…Ke1 4.Rf4 etc.) 4.Rb5 Kd1 5.Rb1, or 2…Ke1 3.Rf5 Kd1 4.Rf1. And 1…f5 [b] compels 2.Rc4 [B] f4 3.Rxf4 Kc1 (3…Ke1 4.Rf3 etc.) 4.Rb4 Kd1 5.Rb1, or 2…Ke1 3.Rf4 Kd1 4.Rf1. Termed the Vladimirov theme, this move pattern contains a paradoxical element. In the first try, 1…f6! [a] disables 1.Rc5? [A], yet post-key, 1…f6 [a] enables 2.Rc5 [A]; and in the second try, 1…f5! [b] disables 1.Rc4? [B], yet post-key, 1…f5 [b] enables 2.Rc4 [B]. In each case, the same position is reached but White fails if it’s white-to-play, and succeeds if it’s black-to-play, meaning this problem demonstrates mutual zugzwang twice.