Rotational twins

The twinning device typically involves adjusting certain pieces in the diagram to create a second position for solving, given the same task. Rotational twins are a more curious type where new positions arise from rotating the whole diagram by 90° or more increments. Such additional arrangements preserve the relative placements of all the pieces, but usually exploit the changed directions of the pawns to produce non-equivalent solutions. For this selection, I shall focus on thematic examples that utilise the rotational shifts intensively, or feature the three special chess moves. These special moves are pawn promotion, en passant capture, and castling, all of which depend on board orientation to be playable.

It is rare to see a mate-in-1 problem that employs no trickery but still makes a point. The four positions are solved by distinct, non-symmetrical moves by the white queen, yet the solutions give the impression of the piece going to the same square: (a) 1.Qd3, (b) 1.Qd3, (c) 1.Qd3, and (d) 1.Qxd3. An amusing piece of work.

Part (a) contains two thematic tries. 1.Rh7? threatens 2.Qe7, but 1…0-0-0! hides the king. 1.Rf1? makes a different threat, 2.Qxd7, but 1…0-0-0! again refutes. The castling key 1.0-0! (2.Qxd7) clears the 1st rank for the rook so that 1…0-0-0 is answerable by 2.Rc1. The self-block 1…Rd8 allows 2.Qf7, while 1…Kd8 doesn’t stop the threat, 2.Qxd7. In (b), castling is ruled out for both sides, but 1.Rc8? (2.Qxe2) remains a try, one defeated by another special move, 1…g1=S! Here the key 1.Ra2! (2.Qd2) provokes a further promotion in 1…e1=Q 2.Qc2 (a mate transference relative to 1…Rd8 2.Qf7 in the first part). And 1…Ke1 2.Qxe2 is unchanged from the other phase. This two-mover reveals an odd choice in its construction: White's bishop on h8 is just a plug with no purpose except to prevent cooks like 1.Qxd7+ Kxf8 2.Rh8. The piece could be replaced by a black pawn on h7, without affecting the solutions or the try play.

In this series-helpmate, the black king has access to two flights, of which f5 could be covered by a knight mate on d6. Black needs to self-block the other one on f3 with a promoted piece. 1.d4 2.dxe3 3.e2 4.e1=S 5.Sf3 Sbd6. The remaining twins follow the same plan, but see the pawn promoting to different pieces: (b) 1.e4 2.e3 3.e2 4.e1=B 5.Bc3 S7f5, (c) 1.d3 2.d2 3.d1=R 4.Rd6 5.Rf6 S2c4, and (d) 1.e3 2.e2 3.e1=Q 4.Qc3 5.Qc6 Sge3. The Allumwandlung theme is carried out by one pawn that promotes on all four edges of the board. A classic miniature using minimal black force.

White’s castled position gives a big hint for the first part: retract 1.0-0 and play 1.Rh3. This is an ideal-mate where every square next to the black king is guarded only once, and all units on the board take part in the confinement. In (b), the king has flights to d5, e6, and e5 – the last one is especially hard to deal with. The solution is to retract 1.dxe6 e.p. and play 1.Rd8, which obtains another attractive ideal-mate. Here White exploits a peculiar property of en passant to uncapture a self-blocking pawn on e5, a square not initially occupied by the retracting unit. Two of the special chess moves are neatly presented, both as white play that must be taken back.

The rotational twinning in our final example is paradoxical, given that pawns and castling option are both absent, and yet the two solutions are not mere reflections of each other. Part (a) is solved by 1.Ra7+! Kxb8 2.Sc6. For (b), the expected sequence 1.Rg8+ Kxh7 2.Sf6 is invalid, because the position is illegal with White to play! Black couldn’t have just played …Kg8-h8 or …Kg7-h8, as the king would have been in an impossible double-check either way. Compare with the first position which is legal with White to play, because Black’s last move could have been …Ka7-a8, preceded by the promotion double-check, b7-b8=B+. As discussed in a previous blog, Deceptive mate-in-one problems, such a situation in (b) is resolved by a special convention: the position is deemed Black to play, making it legal. After Black’s only move …Kxh7, White delivers mate-in-2 by 1.Sf6+ Kh8 2.Rg8. Thus a hidden retro element distinguishes the two positions, and the two solutions also show an AB-BA reversal of white moves.

Who created half of this classic three-move miniature?

10 Feb. 2025