In chess problems, retrograde analysis is a technique employed to determine which moves were played leading up to a given position.
Other problems may ask specific questions relating to the history of the position, such as, "Is the bishop on c1 promoted?".
This is essentially a matter of logical reasoning, with high appeal for puzzle enthusiasts.
The solver is required only to deduce a legal sequence of moves which lead to the position, regardless of any considerations of chess strategy.
"[1]In the problem on the left, if the rook on f3 is a promoted piece, then it is possible to prove that Black cannot castle.
But only the b- and e-pawns could have promoted there, and either would require at least seven captures to account for the positions of the White pawns, when only six Black units are missing.
Now White must remake the battery on the d-file to give mate, which seems possible via either 1.0-0-0 or 1.Rd1.
[2] This is perhaps the most controversial of the retrograde analysis conventions; if it is employed, the problem is usually marked as "AP".
In this case, the en passant capture is made, then its legality is proved a posteriori; this is accomplished by castling.
In some such problems, Black's defence consists of trying to prevent White from castling, rendering the initial en passant capture illegal.
Nenad Petrović composed several problems in this vein; the example given on the left was discussed extensively in Tim Krabbé's book Chess Curiosities.
The solution as originally given was 1.fxg6 ep (intending to prove its legality a posteriori by castling) 1...Bc5 (preventing castling and threatening ...Bf2+, which would force a king move and delegitimize the en passant capture) 2.e3 fxe3 3.0-0 (sacrificing a rook in order to legitimize the en passant capture; if 3.d4 Bb4+ forces a king move and prevents castling) ...e2+ 4.Kg2 exf1=Q+ 5.Kxf1 and White has a won position.
This composition was highly controversial when first published, due in part to the "non-chess" motivations behind the moves 1...Bc5, 2.e3 and 3.0-0, and provoked heated debate in chess problemist circles.
Amid the controversy, it was overlooked that the win is not clear in the final position, and in fact Black could have won with 3...exd2+!
Raymond M. Smullyan wrote two well-received retrograde analysis riddle books: