The Retroanalysis is not used to solve direct mate problems, but there is a category of proof (or retro) problems, which are depending on it.
An important branch of retroanalytical problems is the Shortest Proof Game (SPG).
The Retroanalysis is a subcategory of Fairy Chess.
The retroanalytical problem may have stipulation “White plays and mates in 2 moves” and the essence of the problem may not be in the solution but in the history of the position. We may find there the answers in some basic questions and only then we may proceed to reach the solution.
(1) Is the position legal?
(2) Is there right for castling?
(3) Is there right for capturing en passant a pawn?
For example, an orthodox position is illegal when there are eight white Pawns and three white Rooks. Where did we find the third Rook, since we have not promote a Pawn?
If there is right to capture a Pawn en-passant, then this capture may be used as key-move. (We have already seen such a problem).
The stipulation of a retro problem may contain a specific question, such as 'Is Ac1 a promoted piece?'
Basically, all these are the object of logical conclusions and give a pleasant time to chess puzzle solvers.
 | (Problem 110) Sam Loyd, Musical World, 1859 White plays and mates in 2 moves #2 (2+4) retro |
| [r3k3/p1p5/Q3K3/8/8/8/8/8] | |
The first need for retrograde analysis appeared in a problem of Sam Loyd, which was published in 1859 in the magazine 'Musical World'. The solution is as follows:
Key : 1.Qa1! ~ (black plays at random) 2.Qh8#
Some solvers objected that after the defense 1...0-0-0 (Queen's side castling) of the Black there is no mate in the second move. The argument of the composer was that Black has no right to defend this way. It is quite obvious from the position of the problem that the previous black move was a move by the King or by the Rook, and that means Black has lost the right for castling.
Full retrograde analysis
 | (Problem 111) Eric Angelini, Europe Echecs, 1995 Black is to move. What was the last move of the white? (Retroanalysis) W(-1)? retro |
| [8/8/3r4/4K3/8/4kqpb/8/8] | |
In the problem of Eric Angelini, published in 1995 in the magazine ‘Europe Echecs’, we see that the target of the problem is exactly the retrograde analysis, that is the solver must find the previous move of the white ( notation : W(-1) ).
With a shallow examination there is no apparent solution : From whichever square came the white King to e5, he was already threatened by two opponent pieces (which is impossible!). Anyway, after a little thought, we discover that if the wK came from f5, then the previous black move could be f4xg3 e.p., (that is the bPf4 has captured wPg4 en-passant), so, before f4xg3, white should have played g2-g4.
But which piece had the black moved before that? (The wK on f5 were under check from the bB on h3, and there was a wP on g2).
The only possibility is that a black Knight has moved from g4 to e5 giving discovered check. And exactly this bS has been captured by the wK moving from f5 to e5. We cannot find any other previous moves with absolute certainty.
Summarizing, the last moves (the last four half-moves) before the given position were :
(1)...Sg4-e5+ (discovered check)
(2) g2-g4 f4xg3 e.p. + (double check)
(3) Kf5xe5
Symmetry is invalidated with retroanalysis
 | (Problem 155) T. R. Dawson, 1914 Mate in 2 moves (retroanalysis) #2 (11+6) retro |
| [4k3/1p2P2p/2S1P1S1/2PpKpP1/3PpP2/4P3/4P3/8] | |
You have probably seen again the problem-155, by Dawson, which is symmetrical. On first sight seems that the last black move may be d7-d5 or f7-f5, thus the white begins with an en-passant capturing key
from the queen's side (1.cxd6 [2.d7#]) or
from the king's side (1.gxf6 [2.f7#]).
Are both continuations correct?
No! We can prove that by examining the skeleton of the white Pawns.
Pawns e3-f4-g5 came from squares f2-g3-h4 capturing three black pieces.
Pawn e7 came from square a3 capturing four black pieces.
Pawn e6 came from square b3 capturing three black pieces.
Totally, ten black pieces were captured from Pawns trying to construct the skeleton in the given position.
In the diagram there are still six black pieces, thus all the missing black pieces were captured by white Pawns.
This is especially valid for the black Bishop of c8. Some previous moment it left its initial position and it went elsewhere (in the rows 3, 4, 5, or 6) to be captured by a white Pawn. But, in order to free Βc8, obviously the black Pawn d7 opened the way.
Thus d7-d5 was not the last black move!
Key : 1.gxf6!
1...~ (black plays one of the six available moves)
2.f7#
(This post in Greek language).
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