“Open problems” in proof games

The latest issue of the German problem magazine feenschach contains an article named “A compilation of some fascinating open problems in the Proof Game genre,” by the French expert Nicolas Dupont. He proposes more than fifty “open problems” or composing tasks indicative of the ultimate ideas that could be achieved in proof games. These are challenges inspired by existing proof games that demonstrate some sorts of record effects, and your goal is to better them or to accomplish some related tasks. The article cites sixty-two such “extreme” proof games, and here I present two of them.

Many established themes in proof games relate to pawn promotions. A classic example is the Pronkin theme, in which a piece seemingly on its game-array square turns out to be a promoted pawn, replacing the original piece that has been captured. The highest number of such Pronkin pieces to be rendered in a proof game is four, and the best problem to have attained that figure is perhaps the one shown below. Here the four white thematic pieces are remarkably all of different types, so that the Allumwandlung theme is featured as well. The paradoxical white promotions are necessary to assist Black in positioning its pieces in time. Thus White must sacrifice two pieces to the b5- and c6-pawns quite early to allow Black to develop on the queen-side, and this necessitates two promotions to replace the captured pieces. Further, Black has promoted to two minor pieces, and each has time to make only one move after the promotion, viz. …Sg1-h3 and …Bd1-h5. To facilitate this plan, White must leave the original g1-knight and d1-queen to be captured on their home squares by the promoting pawns. Consequently, White must promote two more pawns to substitute for these pieces.

The solution is 1.e4 a6 2.Bb5 axb5 3.h4 Ra6 4.h5 Rg6 5.h6 Sf6 6.hxg7 h5 7.a4 h4 8.a5 h3 9.a6 h2 10.a7 hxg1=S 11.Ra6 Sh3 12.Rc6 dxc6 13.e5 Kd7 14.e6+ Kd6 15.exf7 e5 16.f4 e4 17.f5 Ke5 18.g8=B Bc5 19.f8=S e3 20.Bc4 Be6 21.a8=R Sd7 22.Ra1 Qa8 23.Sh7 Rd8 24.Bf1 Se8 25.f6 e2 26.f7 exd1=B 27.f8=Q Bh5 28.Qf3 Bb3 29.Qd1 Kf4 30.Sg5 Se5 31.Sf3 Rdd6 32.Sg1. So the a1-rook, d1-queen, f1-bishop, and g1-knight are all promoted – an incredible conception showing tremendous technical skill on the part of the composers. The open problem in this case is not to improve on the composition (that might be impossible!), but to realise other combinations of four-fold Pronkins, such as two white and two black rook promotions.

Not all of the proof games discussed in the article are “blockbusters” like this promotion extravaganza. Others display more elegant types of themes but which still involve a maximum task of some sort, as in our second selection. In proof games with two solutions, a difficult changed-play scheme consists of a player castling in one sequence of play but not in the other, with both options leading to the same diagram position. Mark Kirtley’s problem doubles this idea, impressively bringing about a reciprocal change of castling between White and Black. 1.c4 Sf6 2.Qc2 Sh5 3.Qxh7 f5 4.Qxg7 Bxg7 5.Sf3 Bxb2 6.Bxb2 Kf7 7.Bd4 Re8 8.Bxa7 b6 9.Sd4 Bb7 10.Sb3 Bxg2 11.Bxg2 Kg8 12.Bc6 Sxc6 13.0-0 Rb8 14.Kg2, and 1.c3 Sf6 2.Qc2 Sh5 3.Qxh7 f5 4.Qxg7 Bxg7 5.c4 Bxb2 6.Bxb2 0-0 7.Bd4 Re8 8.Bxa7 b6 9.Sf3 Bb7 10.Sd4 Bxg2 11.Sb3 Bxf1 12.Kxf1 Sc6 13.Kg2 Rb8 14.Rf1. The challenge inspired by this work also seems very hard to fulfil: construct a two-solution proof game in which White makes an en passant capture in one phase, and Black does so in the other.

You can view the complete “open problems” article as a free PDF-file from the feenschach site.