Written by Michael McDowell
Retrograde Analysis (RA) is a term referring to the deduction of the play in the imaginary game leading up to a position in order to determine, for example, which side is to play, whether or not the position is legal, is castling still possible or what was the last move played. A number of types of problem involve retrograde analysis.
(1) T. R. Dawson
Falkirk Herald, 1914
Mate in 2
Legality of position is a basic convention of orthodox chess problems, and as such RA can be used to solve some directmates. In Dawson's asymmetric the white pawns have made ten captures, accounting for the missing black pieces. The black king could not have moved last from d7 or f7, as the e6 pawn could not have checked on the previous move, so the only possible last moves are Pd7-d5 or Pf7-f5. In each case an en passant capture will mate in two, however Pd7-d5 must have happened earlier in order to free the c8 bishop to be captured, therefore Pf7-f5 is the only possible last move and 1.Pxf5 e.p. solves.
(2) Axel Åkerblom
Svenska Dagbladet, 1925
Mate in 2
RA sometimes features in less serious directmates. In 2 with White to play there is no solution; however Black cannot have moved last, so it is his turn to move, and each of his four possibilities leads to a different mate in 2. The moves fxe6, f6, f5 and Kxg1 lead to 1.Sh3, 1.Sf3, 1.Kf2 and 1.Rf6 respectively.
(3) W. Langstaff
Chess Amateur, 1922
Mate in 2
In 3 it is clear that Black's last move was either Pg7-g5 or a move by the king or rook. If it was the pawn move then 1.Ke6? fails to 1...O-O and the problem solves by 1.Pxg5 e.p. threatening 2.Rd8, with the variation 1...O-O 2.h7. If king or rook moved last then castling is clearly illegal and the problem solves by 1.Ke6 any 2.Rd8.
This is a simple illustration of Partial Retrograde Analysis; the last move cannot be determined precisely, so both possibilities are considered separately. Such problems often have PRA added to the stipulation as a guide to the solver.
A Shortest Proof Game (SPG) is the shortest sequence leading from the initial game array to the given position.
(4) Richard Müller
SPG. Position after White's 7th move.
In the simple looking 4 the natural attempts to use the white queen and black bishop to capture the missing pieces are doomed to failure (try it!). The surprising solution reveals that the queen is actually a promoted pawn! 1.a4 d6 2.a5 Bg4 3.a6 Bxe2 4.axb7 Bxd1 5.bxa8Q Bg4 6.Qf3 Bc8 7.Qd1
(5) Tibor Orbán
Die Schwalbe, 1976
Position after Black's 4th move.
Slightly different are positions which must be reached on a specified move.
The position of 5 is easy to reach after Black's third move, by 1.e4 e6 2.Bb5 c6 3.Bxc6 dxc6 (Black's first two moves can be transposed), however reaching the position after Black's 4th move is rather tricky! The surprising solution involves a hidden switchback: 1.e4 e6 2.Bb5 Ke7 3.Bxd7 c6 4.Be8 Kxe8.
(6) John D. Beasley
The Problemist, 1972
What was White's first bishop move?
A number of retros ask the solver to determine a specific move.
In 6 the choice would appear to lie between Ba3 or Bb2. Examination of the position reveals that the c8 bishop was captured on its home square and therefore the g6 bishop is the promoted e-pawn. The pawn must have promoted on b1 from a2, as promoting from b2 would have meant that the bishop could never have escaped past the b3 pawn. The pawn made five captures, but if promotion took place before the c1 bishop moved there would only have been four pieces available for capture, namely the a-rook, the a-pawn and the two knights. Both white bishops must have been captured on their home squares in order to release the queen and h-rook for capture. The bishop at c1 is the promoted a-pawn, which must have promoted at b8, as not enough captures are available for promotion at d8. Hence White's first bishop move was Bb8-a7.
Retractors are problems in which a number of moves are retracted from the diagram then forward moves are played from the new position. They may or may not involve retrograde analysis.
(7) W. Naef
Die Tat, 1955
White retracts his last move
and mates in 1
In 7 it looks as though White must mate by playing P(f7)xg8=Q. This involves retracting a promotion at e8, and for the mate to work the retraction must be P(f7)xB(e8)=R. One of the black bishops is clearly a promoted pawn, however the black pawns have made 8 captures, accounting for all the missing white pieces with the exception of the two bishops, which were captured on their home squares. No piece is left for the promoting black pawn to capture on b1 or d1, so the attempted solution is illegal!
The less obvious possibility is for the king to retract a move from e6. As the bishop could not have moved on to the line to give check, the retracted move must be K(e6)xS(e5), the knight having come from f7 on the previous move. White then plays Rxg8 mate.