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

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!

• If you have fun with these kinds of chess puzzles, I warmly recommend matplus.net, a forum for chess problem composers. At last they rather need only several minutes for solving :-) Commented Mar 26, 2022 at 14:31

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 :-)

• @CarloWood: In the chess problem genre your puzzle fits in, it is usually preferred when the solution is absolutely unique. Here, for example, you could have replaced f3 by h3+Rh2 (and some black move, it's a random example) so that White gets just right in time. The Bc8 could capture a White piece just for fun to make its way unique too. Of course the fact that it returns to c8 is a great plus. I'll show the problem to the experts, maybe they find a way. Commented Mar 29, 2022 at 7:50

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.