I wouldn't be surprised if there is a way of doing it in 4 guesses (3 to identify and a 4th that's known to be right), although you probably need to adjust the later guesses based on the results of the first. It wouldn't be impossible to search the space of strategies exhaustively. Precomputing the score function (and storing it as 4096*101 4096-bit bitstrings for efficient set intersection) would speed things up, and it could be a chance to use the 3D texture handling features of a GPU (I've done very little GPU programming so take my enthusiasm with a pinch of salt).