That was fun - but your puzzle does not have a single solution.
Here are three solutions that I found - and something tells me you found another one (because in this case it is trivial you can't know where the black knight ends).
[FEN "rnbqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBQKBNR w KQkq - 0 1"]
1. Nf3 e6 2. Nc3 Ba3 3. bxa3 Nc6 4. Rb1 Nd4 5. Nxd4 b5 6. Rxb5 Qh4 7. Nb3 g5 8. Rxg5 Qh3 9. gxh3 Nh6 (9... Nf6) (9... Ne7) 10. Na1 Rb8 11. Rgg1 Rg8 12. Nb1 Rb3 13. axb3 Rg3 14. hxg3
Pieces taken: Two rooks (10 points), a bishop (3 points), a knight (3 points), a queen (9 points) and two pawns (2 points). 10 + 3 + 3 + 9 + 2 = 27.