In the game 2048, you are given a board of tiles bearing numbers which are powers of 2. At each turn, you shift all the tiles in a given direction and are given a new tile; if two tiles bearing the same number are shifted into each other, they coalesce into one bearing the next power of 2, and that new power of 2 is added to your score.
The score is always displayed at the top of the board while you play, but I'm wondering if it can be deduced from the position of the board itself.
Given a particular layout of the board - these tiles bearing these numbers - is there only one possible score? Or could there be two different ways of playing to achieve that final layout, which give rise to two different scores?
(I don't know the answer to this question.)