There is a variant of the popular game 2048, called 2048 hard or 2048 impossible, which automatically places each new tile in the hardest possible location. Is this variation possible to solve, and if not, what is the highest possible score?
Edit: I guess I should have been a little more clear. First, I want to know if this variation is solvable. Then if the answer turns out to be no, I would like to know what the highest possible score is.
Edit 2: Perhaps I should clarify yet again. This variant contains no element of chance whatsoever, but it would be necessary to know the algorithm used to generate new tiles in order to create a solving algorithm. Then again, if someone has actually beaten the game, that would answer my question. Also, the scoring metric is the one posted in RandomUser's second comment.