Which piece was captured last - knowing that this position was reached in the minimum number of moves possible?

Question

This is a puzzle that I made a while ago, but never really published anywhere before (although I posted it on an obscure Dutch telegram channel).

The question is simple: what was the piece that was captured last? Hence, the answer can be: rook, knight, bishop or queen.

However, you can't know - because there are multiple ways to reach this position - so there is extra information: this position was reached in the minimum number of moves possible.

As answer - just post a game-diagram (PGN) that shows a way to reach the given position in the fastest way possible.

[FEN "rnb1kbnr/p1ppp1pp/1p6/8/4P3/3P1P2/BPP3PP/RN1QKqNR w KQkq - 0 1"]

Have fun!

Answer 1

Full solution attempt:

Last move obviously was exZf1=Q+, with yet unspecified piece Z. If that was original Bf1, a2 is promoted. Impossible, as a2 can only promote on b8 given that it can only promote by a6xQb7-b8 (the black f pawn promoted on f1, as already established, leaving only the black queen as victim for the white a pawn) - wrong color. Thus Ba2 is original and a2 promoted, again by a6xQb7-b8. We thus already know the promoted figure Z is either Q or N (R can't get out again). Here is a N attempt, I have a good hunch that Q is faster (Q-b7-a6-f1) and even the moves are unique.

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]

1. a4 b6 2. a5 Bb7 3. a6 Bc6 4. e4 Qc8 5. Bc4 Qb7 6. axb7 Na6 7. b8=N Bb7 8. Nc6 f5 9. d3 f4 10. Be3 fxe3 11. f3 e2 12. Nd4 Nb8 13. Nf5 Bc8 14. Ng3 Bb7 15. Ba2 Bc8 16. Nf1 exf1=Q+

A simple counting of White moves proves that a N solution can't be improved. Q could attain 14 moves, here Black also needs 14 moves minimally - so this could work out if timed carefully. But I don't see a trick to actually save the one black move: with a square z5, I could play Bz5 and avoid wasting the white/black tempo, so I am at 15.

[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]

1. a4 b6 2. a5 Ba6 3. e4 Bb5 4. Bc4 Qc8 5. a6 Qb7 6. axb7 Nc6 7. Bb3 Ba6 8.
b8=Q+ Bc8 9. Qb7 f6 10. Qa6 f5 11. Qf1 f4 12. d3 Nb8 13. Be3 fxe3 14. Ba2 e2
15. f3 exf1=Q+

Optimality proof attempt: White obviously does need 14 moves (one tempo was wasted on Bb3). But then let's retro-move further from the final diagram: White can only take back "neutrally" f3. But another move pair is needed before Be3, which forces d3 before that, and the white queen can't get to f1 anymore! White has no such move, obviously, so a tempo like Bb3 must be inserted.

5 minutes for the logic :-)

Answer 2

The last piece captured was a white knight on f1.

• The last move must have been exf1=Q.
• With a bishop on a2, the captured piece on f1 must have been promoted before.
• It is white's a-pawn then that must have reached b8 via a6-axb7-b8.
• Promotion to rook or bishop can be excluded since they cannot return to f1 in above pawn structure.
• Promotion to queen can be excluded wrt the condition of minimal game length.