An “extraordinary” moment in Gukesh-Ding WCC Game 13 and knight-switching proof games

During Game 13 of the World Championship match between Gukesh and Ding, I was watching the livestream on Chess24 where the commentators (both terrific) were GM Peter Leko and GM Daniel (Danya) Naroditsky. When Gukesh played 15.Sh5 (see diagram below), an eagle-eyed Leko pointed out that this knight on the right-edge came all the way from b1 while the knight standing on c3 originated from g1. The two commentators were amused as well as amazed by such an unusual occurrence, with Leko calling it “extraordinary” and Danya saying his mind is blown. As a problemist I was reminded of certain proof game compositions where two equivalent pieces must paradoxically switch places, to attain a position as quickly as possible. Then to my surprise Danya expressed a similar thought.

Referring to such problems as “chess riddles,” Danya tried to recall a famous 4-move proof game in which a black knight from g8 ended up on b8. He began to outline the final position as having black pawns on c6 and e6, but that’s incorrect as he apparently fused two distinct classic 4-move games. The well-known one with such black pawns is P0000811 created by Tibor Orban, and it features a different idea. He was accurate, though, in the rest of his description which fits another famous composed game by Ernest C. Mortimer, one in which a knight travels to its counterpart’s original square. Let’s take a look at this problem and other examples that develop the theme.

In proof game problems, the objective is to reach the diagram position from the opening array in the fewest possible moves, disregarding whether such moves are sensible or not. In this case, four moves (by each side) are allowed, and even though the two sides cooperate, there is no straightforward way to capture both of the ostensibly missing g-knights. For instance, 1.Sf3 Sh6 2.Sd4 Sf5 3.Sxf5 d5 4.Sd6+ Qxd6 clearly leaves the queen in the wrong spot. The surprising solution entails the capture of Black’s b-knight instead, meaning the piece on b8 is an impostor from g8. 1.Sf3 d5 2.Sd4 Sf6 3.Sc6 Sfd7 4.Sxb8 Sxb8. Here the move order is imprecise (alternative play like 2.Se5 is possible), reflecting the problem’s early origin when such duals were inconsequential. Modern conventions require proof games to be solved by an exact sequence of unique moves.

Mortimer’s composition is such a gem that it’s worthwhile to modify it to satisfy modern standards of soundness. The version above thus has a uniquely forced solution, 1.Sf3 e5 2.Sxe5 Se7 3.Sxd7 Sec6 4.Sxb8 Sxb8. Another advantage here is the striking diagram position that displays a double homebase set-up, i.e. all uncaptured units of both players are (apparently) on their game-array squares.

Today we call Mortimer’s deceptive manoeuvre the Sibling theme, in which a knight (or a rook) on its home square turns out to have been replaced by its counterpart from the other side of the board. Proof game composers have elaborated on the theme in various ways, and my own take on it is shown below.

Black is missing a knight and the d-pawn while White is missing a knight and the c1-bishop. One obvious way to account for both pairs of doubled pawns is to sacrifice Black’s g-knight on f3 and White’s b-knight on h6, but this proves inefficient, e.g. 1.Sc3 d5 2.Sxd5 Sf6 3.Se3 Sg4 4.Sf5 Se5 5.Sh6 Sf3+ 6.exf3 gxh6 7.Bc4 Bg7 8.d3 0-0 9.Bb5 f6 and White’s c1-bishop cannot be removed in time. Black actually needs to sacrifice the original b-knight on f3 (taking three moves instead of four) to help speed up White’s development, which in turn enables the c1-bishop to be captured on h6 quickly. This plan necessitates three extra moves to transfer the g8-knight to b8, leaving Black with no time to move the d-pawn. If White attempts to use the original b-knight to capture this d7-pawn, it would take four moves which is too slow, e.g. 1.Sa3 Sc6 2.Sc4 Se5 3.Sb6 Sf3+ 4.exf3 Sf6 5.Sxd7 Sxd7 6.Bc4 Sb8 7.d3 f6 8.Bh6 gxh6 9.Ba6 Bg7 10.Bb5+ and the check prevents 10…0-0. White must in fact use the original g-knight to remove the pawn on d7 (in just three moves) – and sacrifice the piece there – so as to facilitate Black’s development. 1.Sf3 Sc6 2.Se5 Sd4 3.Sxd7 Sf3+ 4.exf3 Sf6 5.Bb5 Sxd7 6.d3 f6 7.Bh6 gxh6 8.Sc3 Bg7 9.Se2 0-0 10.Sg1 Sb8. Hence both White and Black execute the Sibling theme.

In the Gukesh-Ding game, both white knights are still on the board in the curious position where they have swapped sides. This raises the question of whether there are piece-switching proof games that resemble such a situation more closely – that is, both knights of a player are still present but they have finished up on the original squares of each other. This difficult effect, even more paradoxical than the Sibling theme, has indeed been accomplished a number of times. Below is a great example where the black knights play the principal roles.

The white units that are shifted from their home squares have used up all 12 moves available. The rook from a1 in particular took four moves, Rc1-c3-f3-f6 – a route that precludes an early Pf4 (not Rd1-d6-f6 because of the obstructing d2-knight). White’s missing d-pawn was thus captured unmoved; Black must use the g-knight to remove it quickly and release White’s queen-side pieces. 1.c4 Sf6 2.Qa4 Se4 3.Qc6 Sxd2 4.e4. After 4…Sb3 (avoiding a check on f3) 5.Bh6, White’s remaining sequence is strictly determined regardless of what Black does. And since the eventual rook move to f6 will hamper access to g8 by a knight, Black has to prioritise a knight trek to that original square. Now if we choose the knight on b3 for this trip, its quickest route will still cause a traffic jam on f6, e.g. 5…Sd4 6.Sd2 Sf5 7.Rc1 Se3 8.Rc3 Sd5 9.Rf3 Sf6 10.Rxf6?? Therefore the b8-knight has to take over the job, being able to reach f6 faster. 5…Sa6 6.Sd2 Sb4 7.Rc1 Sd5 8.Rc3 Sf6 9.Rf3 Sg8 10.Rf6. There’s just time left for the b3-knight to move to b8 and complete the switch of the two black pieces. 10…Sc5 11.f4 Sa6 12.Sgf3 Sb8. Of all the proof games achieving this exchange-of-places theme, this one is perhaps the most elegant. Not only does the diagram position present an eye-catching initial array for Black, but the game is also very economical, both in length (12 moves only) and in the number of captures (just a pawn missing).