Solutions for "Homebase" (aka "At Home") Proof GamesThe first couple of problems exhibit the Pronkin theme (a promoted piece moves to the homebase of a captured piece of the same kind). The others combine Pronkin with Ceriani-Frolkin (the capture on a particular square of a piece promoted on a particular square.) In parenthesis, am I the only one to find something poignant in the Ceriani-Frolkin theme? Something about the yearning quest for identity against the cruel backdrop of life's short span. Sigh. Anyway. My own guidelines for these tasks is to attempt to achieve them with the minimal number of moves, and within this constraint to attempt the minimum number of captures. Other themes which naturally come up in this context are:
Thierry Le Gleuher has composed many of these problems, and has a different aesthetic, which is to attempt to achieve these positions with the maximum number of moves. This gets too close to "massacres" for my current tastes. All of these are verified by Natch or Euclide. I have kept a copy of the output file for the very time-consuming ones. See also the Pronkin & Ceriani-Frolkin analysis further down this page. {C01} 1. h4 g5 2. h×g5 Nf6 3. g×f6 Bg7 4. f×e7 Rf8 5. e×f8=B B×b2 6. Ba3 B×c1 7. B×c1.Minimal possible number of moves for B Pronkin, and smaller number of captures than {CP04}. (C+) {C02} 1. e4 d5 2. e×d5 Nc6 3. d×c6 Qd4 4. c×b7 Q×b2 5. b×a8=Q
Q×c2 6. Qf3 Q×d1+ 7. Q×d1. {C03}1. b4 h5 2. b5 h4 3. b6 h3 4. b×a7 h×g2 5. a×b8=N g×h1=N
6. N×d7 Ng3 7. Ne5 N×e2 8. Nf3 N×g1 9. N×g1. {C04}
{C05} 1. h4 d5 2. h5 d4 3. h6 d3 4. h×g7 d×c2 5. g×h8=Q c×b1=Q
6. Qd4 Qd3 7. Q×d8+ Q×d8. {C06} 1. g4 b5 2. g5 b4 3. g6 b3 4. g×h7 b×a2 5. h×g8=R a×b1=N 6. R×g7 N×d2 7. R×f7 Ne4 8. Rg7 Nf6 9. Rg8 N×g8. N Pronkin + R Frolkin. Length 2 Donati switchback & Phoenix. (C+) {C07} 1. g4 d5 2. g5 d4 3. g6 d3 4. g×h7 d×c2 5. h×g8=N c×b1=B
6. N×e7 Bf5 7.N×c8 B×c8. {C08} 1. h4 f5 2. h5 f4 3. h6 f3 4. h×g7 f×e2 5. g×h8=Q e×f1=R+
6. Ke2 R×f2+ 7. Ke1 R×d2 8. Qd4 R×d1+ 9. Q×d1. {C09} (a) 1. f4 h5 2. f5 h4 3. f6 h3 4. fxe7 hxg2 5.
exf8=N gxh1=R 6. Ng6 Rxh2 7. Nxh8 Rxh8. {C10} 1. b4 d5 2. b5 d4 3. b6 d3 4. b×a7 d×c2 5. a×b8=Q c×b1=B
6. Q×b7 Bf5 7. Q×c8 B×c8. {C11} 1. g4 c5 2. g5 c4 3. g6 c3 4. g×h7 c×b2 5. h×g8=N b×c1=Q
6. N×e7 Q×c2 7. Nd5 Q×a2 8. Nc3 Q×b1 9. N×b1. {C12} 1. a4 g5 2. a5 g4 3. a6 g3 4. a×b7 g×h2 5. b×c8=B h×g1=R
6. Bb7 R×g2 7. B×a8 R×f2 8. Bg2 R×f1 9. B×f1 {C13} 1.f4 c5 2.f5 c4 3.f6 c3 4.f×g7 c×b2 5.g×h8=R b×c1=B
6.R×h7 Bb2 7.R×f7 Bbg7 8.R×f8+ B×f8. {C14} 1.d4 a5 2.d5 a4 3.d6 a3 4.d×c7 a×b2 5.c×b8=R b×c1=Q
6.R×b7 Q×b1 7.R×d7 Qbb6 8.R×d8+ Q×d8. {C15} 1.b4 h5 2.b5 h4 3.b6 h3 4.b×c7 h×g2 5.c×d8=B g×f1=N
6.B×e7 N×h2 7.Bf6 Ng4 8.R×h8 N4×f6 9.R×g8 N×g8. {C16} 1.b4 f5 2.b5 f4 3.b6 f3 4.b×a7 f×e2 5.a×b8=R e×d1=R+
6.Ke2 R×d2+ 7.Ke1 R×c2 8.R×c8 Rc×a2 9.R×a8 R×a1 10.R×a1. Minimal Representations of the Pronkin Theme A lower bound on the number of moves is 4.5 + the return time of the prodigal promoted Pronkin. The queen cannot return in 1 move without checking. Nor apparently can the rook return in 1 move, so the following lengths are best possible.
Minimal Representations of Pronkin-Frolkin Pairs The shortest Pronkin-Frolkin compositions can be laid out in the following diagram, according to which piece is the Pronkin promotee (row) and which piece is the Frolkin promotee (column) In none of the known examples is the Pronkin promotion Donati. In every known case, it is the Pronkin promotee which captures the Frolkin one, and in every case except {C15}, this is the final move.
The following table shows the best values to date.
Except possibly for NR, NB & RR, I don't think any further improvement is possible. Here's my reasoning. The Pronkin lower bounds given before still apply, but the key issue for the Frolkin piece is that we must prove its identity before it gets captured. It can do this by moving, or by having the opposing king move near it. A Frolkin Q must move twice to prove it's identity. If a Frolkin B/N moves it leaves the back rank, so either it or its capturer must spend another move returning to the 8th rank. So 7.0 is the minimum number of moves for Frolkin Q/B/N. The Frolkin rook is more complicated. One approach is for it to move and at some point have the opposing king remain calmly a bishop's move away from it, thus demonstrating that the piece is not a queen. On the other hand, the rook may main stationary, and the Black king may remain (i) a bishop's move away (ii) a knight's move away, thus demonstrating by elimination that the unit is a rook. Except for situations difficult to engineer in the homebase environment, it seems that we must allow for three rook moves after promotion. This gives a minimum of 8.0 moves for the rook case. {C17} 1. Nc3 Nf6 2. Nd5 Ne4 3. N×e7 Nc3 4. Nc6 Qg5 5. N×a7 Qb5
6. N×b5 Ba3 7. N×a3 Nb1 8. N×b1 {C18} 1. e4 Nc6 2. e5 N×e5 3. Bd3 N×d3+ 4. Kf1 N×c1 5. Qg4 N×a2
6. Qb4 N×b4 7.Ra6 N×a6 8.Ke1 Nb8 {C19} 1. c4 a5 2. Nc3 a4 3. N×a4 R×a4 4. Qc2 R×c4 5. Q×h7
Rh4 6. Q×h8 R×h8. And the bonus question... {C0} |