Originals, 1995, Page 2
14 - Eric Angelini Retro Mailing List, 03.08.1995
First of all, the statement of the problem is ambiguous (and Eric tells me this was intentionally so).
"What was Black's 15th and last move?"
I can't solve the problem for Interpretation 1, and I suspect (but haven't proven!) that it's impossible.
I have managed to solve it for interpretation 2 (and Eric confirmed that this was the correct interpretation).
[Incidentally, I'd suggest rewording the problem statement: "Black made 15 moves in this game. What was Black's last move?" I can understand Eric's wishing to disguise the need for White's 16th move, but the problem as stated suggests (to me) that perhaps that is ruled out. I think my wording more clearly leaves open the possibility of White's having made a 16th move without actually stating it explicitly. Maybe its just me, but I'm really bothered when I don't know what the problem statement really is]
Here is one possible game:
1. a3 h5 2. b3 h4 3. c3 h3 4. d3 h3xg2 5. Nf3 g1(N) 6. Ne5 Ng1xe2 7. Nc4 Nd4 8. Qf3 Rxh2 9. Be2 Rxf2 10. Bd1 Rh2 11. Rxh2 a5 12. Ra2 Nc2 13. Bxc2 Ra6 14. Nb2 Rh6 15. Qd1 Rh8 16. Kd2
This achieves the desired position with Black to move! Black's last move was Rh6-h8.
Are other black moves possible, or is this unique?? (it looks pretty unique to me, but I haven't proved it)
Also, if anyone wants to try to PROVE that the white 16th move is NECESSARY, let me know. I'd be happy to share my partial results (I spent lots of time on this, without finding a solution). For example, I think the only chance is for the white pawns to cross-capture (e.g. a2xb3 and b2xa3) to let the h1 rook come to a2 in 3 moves). Lot's more if there is interest. Thanks to Eric for this challenging problem!
[Solution provided by Glenn Iba]
I eventually came up with essentially the same solution as Glenn - there are a number of variations on the theme, e.g. a slight re-ordering of moves allows the black rook to be captured on a2 instead of h2. But the solution remains the same. I believe managed a proof, *assuming* that the white rook arrives on a2 by traversing the second rank. It seems harder to prove that there is no solution involving pawn captures axb3 and bxa3, as there are several different variations which almost work, e.g.
1. g3 h5 2. Nf3 h4 3. e3 hxg3 4. Bd3 Rxh2 5. c3 Rh5(67) 6. Rh4 a5 7. Ra4 Ra6 8. Ne5 Rb6 9. Nc4 Rb3 10. axb3 gxf2 11. Ra2 f1=N 12. Bc2 Nxe3
13. d3 Nc4? <- Bother! c4 occupied and also prevents white's next move
14. Kd2 Na3 15. bxa3 Rh8 16. Nb2
Other attempts involving promoting to a bishop on g1 fail either because of checking the king when capturing f2 and e3, or running out of time when capturing h2, f4, e3.
[Solution provided by Colin Hogben]
15 - Eric Angelini Retro Mailing List, 22.08.1995 Dedicated to Glenn Giba and Colin Hogben
I admit I am stumped. The White king's path from e1 to h8 must pass through h6, the only square on rank 6 not attacked by Black pawns. The shortest path takes 11 moves; adding the pawn move b2-b3 gives 12 moves. (If White were to castle (queenside), the king would save a move (skipping d1), but the rook would use an extra move returning to a1.)
Before the king may leave rank 1, the queen and queen's bishop must move out of the way. Since White made only 18 moves, that leaves 6 moves for this operation: three out and three back.
The bishop must move to a3. If he moves again, then the queen only has one move in which to clear a path for the king--not enough. Therefore the Bishop stays on a3. If the knight moves (to c3), then he blocks the king's path and must move again, not leaving any moves for the queen. Therefore the knight stays on b1. But with b1 and a3 occupied, the queen can not get out of the king's path in only two moves.
Therefore, I don't see how we reach the position shown after only 18 of White's moves.
Now, if the pawn on e7 were missing :), then the answer would be easy: White's last move was Ba3-c1. (After White's king makes a beeline from b2 to h8, Black's king's bishop returns to f8, and White's queen's bishop returns to c1.)
[Solution provided by Wichaya Top Changwatchai]
16 - Eric Angelini Retro Mailing List, 03.09.1995 Dedicated to Top and Joost (Version of No. 15)
The last queen move must be Black's ... Qg7. Also, the queen must have come from h6, unless I missed something again.
17 - Eric Angelini Retro mailing List, 23.08.1995 Dedicated to Don French
The position is actually achievable in 14 full moves, but the white king can lose a tempo by stepping on a3, e.g.
1. Nf3 Na6 Nf3 Nxc1 2. Nc3 Nb4 Nc3 Nb3 3. Nd5 Nxa2 Ne4 Nxc5 4. Nb4 Nxc1 Nc5 Na6 5. Rxa7 Na2 6. Qa1 Nxb4 7. Kd1 Na6 8. Kc1 Rxa7 9. Kb1 Ra8 10. Ka2 Nb8+ 11. Kb3 Rxa1 12. Ne1 Rxe1 Ne1 13. Rg1 Rxf1 14. Ka3 Rxg1 15. Ka2
There are alternative sets of knight moves:
20 - Eric Angelini Retro Mailing List, 06.09.1995 Dedicated to Pascal Wassong
If White just captured using the K or the R, he is not allowed to castle. So assume that the Na1 just captured. It can't have been a bB, neither bR or bQ because of illegal retro-chess. So it was a bNa1. This means that a bP promoted going through one of the squares d2, f2 or h2. d2 & f2 checks the wK which must have moved forbidding castling. So the bP played g3xh2xg1=N. And this N then played Ng1-f3 showing us that the wK must have moved. So white cannot castle if they just made a capture.
[Solution provided by Pascal Wassong]