[Retros] "half" proof games

[Richard Stanley]

An old chestnut (or should it be chessnut?) asks for a game of chess
in which White plays 1.f3 2.Kf2 3.Kg3 4.Kh4, after which Black
(immediately) mates White. What were Black's moves? Supposedly there
are exactly two (essentially equivalent) solutions. This should be
easy for Francois to check. Perhaps there are other interesting
problems of this nature, where one specifies certain moves of the game
and some outcome, such as a checkmate or the final position. In
particular, is there *any* sequence of n White initial moves so that
Black has a unique way to mate White on Black's nth move? (All n Black
moves should be unique.)

Richard