TITLE: Is the game 2048 always solveable?
QUESTION [16 upvotes]: Games got me on math.  I always want to play best.  
I don't know how to answer my question.  My question is : How to show that the game 2048 is (always) solvable>?  Is there any method other than brute force? 
There is a sudko grid and you use arrow keys to move even number, starting near 2, around so that combine to value 2048. Play, it is very fun.

REPLY [4 votes]: It was claimed that the 2048-game is NP-hard in this arXiv preprint: 
http://arxiv.org/pdf/1501.03837v1.pdf