This page contains the moves up to move 10 that determine all the previous moves uniquely in one-sided chess.
The first few moves have too many problems and are omitted (enumerating the problems is the problem). The rest is quite easy.
(all 20 moves of white)
(8 pawn moves, 8 knight moves, 2 rook moves, 1 queen move)
(8 pawn moves, 6 knight moves, 4 bishop moves, 2 rook moves)
(14 pawn moves, 1 knight move, 1 bishop move, 4 rook moves)
5. axb8=N
5. axb8=B
5. axb8=R
5. axb8=Q
5. hxg8=N
5. hxg8=B
5. hxg8=R
5. hxg8=Q
5. Rxa8
5. Rxh8
6. exf8=R#
6. exf8=Q#
6. Bg8
7. Qxd7#
(nothing)
9. g8=N
9. g8=B
9. g8=R
9. g8=Q
(nothing)
425 6. ?~~? f8=Q# 425 6. ?~~? f8=R#
26859642 7. Q~~? d7 #
25083 8. Rg8? ~~ #
70 9. ?d2? d8 #
(nothing)