# Is the game 2048 always solveable?

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.

• What is game 2048? Commented Mar 21, 2014 at 3:33
• gabrielecirulli.github.io/2048 Commented Mar 21, 2014 at 3:40
• jennypeng.me/2048 this is always solvable. I assure you.
– Guy
Commented Mar 21, 2014 at 3:55
• Problem can be posed more generally: When the game is won at small values (like 16) it is always winnable, but at some point must become unwinnable, as some numbers are too large to be made on the board. Given a board of dimensions $n \times m$, what is the smallest target value at which the game cannot be won? Commented Mar 21, 2014 at 22:20
• According to Zermelo's theorem, because 2048 is a finite game with perfect information, a winning strategy exists for either the computer or the player (where the computer is said to "win" if the player does not win). Zermelo's theorem is constructive, and gives a way to determining who has the winning strategy, but it would be computationally intensive. There are very few general tools that are known for these kinds of problems. If you want to see what the game looks like when the computer places tiles intelligently, see: sztupy.github.io/2048-Hard Commented Apr 6, 2014 at 6:27