Meisterwerke

Suppose white can castle. White captures were hxg, gxf, fxe, exd and c6xb7. Black captures were dxcxd (to let the white d-pawn pass without capture). So black's last move wasn't a capture. The only move that will give white a move that'll leave black with a new retro-move is c7-c5 (and white's last move was c6xb7). So if white may castle, black played c7-c5 as last move.

1. dc6! d3 2. OOO! (forced to prove the legality of the en passant capture) d2 3. Rd2 Be6 4.d7#.

Solution by Philippe Schnoebelen