The challenge is to create the longest list of half moves whereby an AI could re-create that list of moves perfectly only given the ending board state and the number of moves.
As example I will first give a short example that does NOT work.
[FEN ""] 1. a3 a6 2. b3
From that final board state, it is impossible to differentiate it from 1. b3 a6 2. a3
And a short example that DOES work
[FEN ""] 1. a3 a6 2. a4 a5
There is no way to get this board state in exactly 2 moves other than what was done here.
Scoring will work as follows 1. +1 point per move 2. +5 points if the game is complete (the last move in the sequence is a check mate)
My best solution so far is
[FEN ""] 1. a4 h5 2. a5 h4 3. a6 h3 4. axb7 hxg2 5. Rxa7 Rxh2 6. Rxa8 Rxh1 7. Rxb8 Rxg1 8. Rxc8 Rxf1
This would score 21 points: 1 point for each of the 16 moves plus 5 points for ending in a checkmate for black.
Note: opening pawns moving 2 spaces instead of one is necessary in this particular solution. A 9 turn game where the pawns each move one space per turn would be undifferentiated from an identical game where pawns open with the two space move and then rooks spend an extra turn making their first capture. Also, the game cannot be extended by slipping in Bxg2 at any point in time for white, because it would be unclear, when looking back, when such a move had occurred, since there are several possible turns for such a move to occur.