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Retrograde analysis is a technique employed by chess problem solvers to determine which moves were played leading up to a given position. In most problems, this technique is not required, but there is a whole genre of problems in which it is an important part; such problems are known as retros.
Retros may ask, for example, for a mate in two, but the main puzzle (at least in modern retros) is in explaining the history of the position. This may be important to determine, for example, if castling is disallowed or an en passant pawn capture is possible. 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.
Sometimes it is necessary to determine if a particular position is legal, with "legal" meaning that it could be reached by a series of legal moves, no matter how bad.
Langstaff_PRA_problem.png
4k2r/8/5B1P/3R1KpP/8/8/8/8
Some problems use a method called "partial retrograde analysis" (PRA). In these, the history of a position cannot be determined with certainty, but each of the alternative histories demands a different solution. The problem to the right by W. Langstaff (from Chess Amateur 1922) is a relatively simple example; it is a mate in two. It is impossible to determine what move Black played last, but it is clear that he must have either moved the king or rook, or else played g7-g5 (g6-g5 is impossible, since the pawn would have been giving check). Therefore, either Black cannot castle, or White can capture on g6 en passant. It is impossible to determine exactly what Black's last move actually was, so the solution has two lines:
- 1.Ke6 any 2.Rd8# (if Black moved the king or rook)
- 1.hxg6 e.p. (threat: 2.Rd8#) 1...O-O 2.h7# (if Black played g7-g5)
Another important branch of retrograde analysis problems are proof game problems.
Raymond M. Smullyan wrote two well-received retrograde analysis riddle books:
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